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문서 제목 일치

• History of Lie theory
  * Sophus Lie—the precursor of the modern theory of Lie groups ...al concepts and theorems on the structure and classification of semisimple Lie algebras
  17 KB (2,525 단어) - 2021년 2월 17일 (수) 03:03

문서 내용 일치

• Combinatorial representation theory
  * Lenart, Cristian. “Combinatorial Representation Theory of Lie Algebras. Richard Stanley’s Work and the Way It Was Continued.” arXiv:1 [[분류:Lie theory]]
  246 바이트 (28 단어) - 2020년 11월 13일 (금) 08:12
• Lie superalgebra
  ...B., and K. C. Pati. “A Quick Proof on Classification of Vogan Diagrams of Lie Superalgebras.” arXiv:1205.1394 [math], May 7, 2012. http://arxiv.org/abs ...Jae-Hoon Kwon. ‘Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras’. arXiv:1505.06602 [math], 25 May 2015. http://arxiv.org/ab
  985 바이트 (120 단어) - 2021년 2월 17일 (수) 02:40
• Algebraic group
  ...raven, Subspace stabilizers and maximal subgroups of exceptional groups of Lie type, arXiv:1606.02326 [math.GR], June 07 2016, http://arxiv.org/abs/1606.0 * Joseph Bernstein, Stacks in Representation Theory. What is a continuous representation of an algebraic group ?, arXiv:1410.04
  618 바이트 (73 단어) - 2020년 11월 12일 (목) 23:12
• Lattice Toda field theory
  * The lattice Toda field theory for simple Lie algebras: Hamiltonian structure and tau-function [http://www.naruto-u.ac.jp * [[affine Toda field theory (ATFT)]]
  410 바이트 (53 단어) - 2020년 12월 28일 (월) 05:03
• Kac-Wakimoto modules
  * Lie superalgebras * Kac V.G., Peterson D.H.: Infinite-dimensional Lie algebras, theta functions, and modular forms. Adv. Math. '''53''', 125–26
  2 KB (214 단어) - 2020년 12월 28일 (월) 05:17
• Lie symmetries of differential equations
  * Kumpera, Antonio. “On the Lie and Cartan Theory of Invariant Differential Systems, II.” arXiv:1511.08703 [math], November * “On the Lie and Cartan Theory of Invariant Differential Systems | Graduate School of Mathematical Science
  1 KB (134 단어) - 2020년 11월 13일 (금) 19:51
• Complete reducibility
  * Iachello, Francesco. “Casimir Operators and Their Eigenvalues.” In Lie Algebras and Applications, 63–74. Lecture Notes in Physics 708. Springer [[분류:Lie theory]]
  797 바이트 (80 단어) - 2021년 2월 17일 (수) 02:00
• Kostant theorem on Lie algebra cohomology of nilpotent subalgebra
  ...explicit formula in terms of <math>W</math> for the dimensions of certain Lie algebra cohomology groups. * Although he worked in the setting of compact Lie groups and their complexifications, the essential point of the corollary is
  2 KB (273 단어) - 2020년 11월 16일 (월) 05:35
• Root system of affine Kac-Moody algebra
  ** roots coming from the simple Lie algebra ** multiplicity is not always 1 but equal to the rank of the simple Lie algebra
  936 바이트 (142 단어) - 2020년 11월 13일 (금) 06:46
• Parthasarathy-Ranga Rao-Varadarajan conjecture
  * [[Tensor product decompositions of representations of Lie algebras]] ...are, Apoorva. 2012. “Representations of Complex Semi-simple Lie Groups and Lie Algebras.” arXiv:1208.0416 (August 2). http://arxiv.org/abs/1208.0416.
  2 KB (253 단어) - 2020년 11월 16일 (월) 05:34
• LieART mathematica package
  ...79 LieART -- A Mathematica Application for Lie Algebras and Representation Theory]
  314 바이트 (38 단어) - 2020년 11월 13일 (금) 00:08
• Nilpotent orbit
  * “Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras.” Accessed November 11, 2015. http://www.ams.org/bookstore-getit * Bourget, Antoine, and Jan Troost. “On the N=1* Gauge Theory on a Circle and Ellipic Integrable Systems.” arXiv:1511.03116 [hep-Th], N
  511 바이트 (52 단어) - 2020년 11월 12일 (목) 05:57
• Modular invariance in math and physics
  ==path integral in string theory== * string theory (symmetries, modular group) has a natural covariant UV cutoff!
  2 KB (282 단어) - 2021년 2월 17일 (수) 02:41
• No-ghost theorem and the construction of moonshine module and monster Lie algbera
  ==background from string theory== * Construction of a Lie algebra from a VOA
  4 KB (564 단어) - 2021년 2월 17일 (수) 02:29
• Birman–Murakami-Wenzl algebra
  ...Ring Theory and Representation Theory, 1–10. Symp. Ring Theory Represent. Theory Organ. Comm., Yamanashi. http://www.ams.org/mathscinet-getitem?mr=2264119. * Benkart, Georgia. 1996. “Commuting Actions—a Tale of Two Groups.” In Lie Algebras and Their Representations (Seoul, 1995), 194:1–46. Contemp. Math
  3 KB (325 단어) - 2021년 2월 17일 (수) 02:38
• 3j symbol (Clebsch-Gordan coefficient)
  [[분류:Lie theory]]
  329 바이트 (24 단어) - 2021년 2월 17일 (수) 02:28
• Root systems and Dynkin diagrams(mathematica)
  [[분류:Lie theory]]
  418 바이트 (40 단어) - 2021년 2월 17일 (수) 03:17
• Weyl group representations on zero weight spaces
  [[분류:Lie theory]]
  677 바이트 (63 단어) - 2020년 11월 13일 (금) 09:41
• Affine mathematica package
  ...for computations in representation theory of finite-dimensional and affine Lie algebras]
  402 바이트 (46 단어) - 2020년 11월 16일 (월) 07:57
• Degrees and exponents
  [[분류:Lie theory]]
  360 바이트 (29 단어) - 2020년 11월 13일 (금) 11:11
• Generalized Cartan matrix
  ==Cartan matrix of a simple Lie algebra== * In semi-simple Lie theory, a cartan matrix is a square matrix
  3 KB (498 단어) - 2021년 2월 17일 (수) 02:33
• Strange identity of Freudenthal-de Vries
  * H. FREUDENTHAL and H. DE VRIES. “Linear Lie groups”, New York: Academic Press, 1969. [[분류:Lie theory]]
  1 KB (125 단어) - 2021년 2월 17일 (수) 02:56
• Harish-Chandra module
  [[분류:Lie theory]]
  419 바이트 (41 단어) - 2021년 2월 17일 (수) 02:07
• Modular representation theory of algebraic groups
  \DeclareMathOperator{\Lie}{Lie} ...gebras over the complex numbers, or even compact real Lie groups. As with Lie algebras, such algebraic groups are classified up to isogeny by their root
  3 KB (499 단어) - 2020년 11월 13일 (금) 04:20
• ODE/IM correspondence
  * Stefano Negro, Lectures on Integrable Structures in Quantum Field Theory and Massive ODE/IM Correspondence, arXiv:1606.02952 [math-ph], June 09 2016 ...mondo, and Daniele Valeri. “Bethe Ansatz and the Spectral Theory of Affine Lie Algebra--Valued Connections. The Non Simply--Laced Case.” arXiv:1511.0089
  2 KB (186 단어) - 2020년 11월 16일 (월) 05:32
• Seminar topics on affine Lie algebras
  ...e.com.au/books?id=_0zyWYJGUakC&printsec=frontcover&dq=Application+of+group+theory+in+physics+and+mathematical+physics&source=bl&ots=q5F83jIVbm&sig=ii3X3aeugp [[분류:Lie theory]]
  760 바이트 (105 단어) - 2020년 11월 16일 (월) 05:28
• 블라디미르 아놀드
  [http://www.institut.math.jussieu.fr/seminaires/singularites/abel.pdf Abel’s theory and modern Mathematics] ...s, partial derivative equations, Lie groups and algebra theory, cohomology theory and scientific computing. Celestial mechanics is the origin of dynamical sy
  2 KB (354 단어) - 2020년 12월 28일 (월) 03:27
• Strong Macdonald theorems
  ...a diagram automorphism twist. These twisted strong Macdonald theorems are Lie algebra cohomology versions of Macdonald's constant term conjecture for twi * [[Lie algebra cohomology]]
  2 KB (335 단어) - 2020년 12월 28일 (월) 05:17
• Elements of finite order (EFO) in Lie groups
  * explicit formulas for the number of conjugacy classes of EFOs in Lie groups * appears for the number of certain vacua in the quantum moduli space of M-theory compactifications on manifolds of <math>G_2</math> holonomy
  1 KB (200 단어) - 2020년 11월 14일 (토) 02:03
• BRST quantization and cohomology
  * [[Gauge theory|gauge theory]] = principal G-bundle * we require a quantization of gauge theory
  6 KB (815 단어) - 2021년 2월 17일 (수) 03:01
• Volume of a compact Lie group
  ...e functions <math>J_\lambda(x)</math> play a central role in random matrix theory. ...ersi, and Peter J. Forrester. “A. Hurwitz and the Origins of Random Matrix Theory in Mathematics.” arXiv:1512.09229 [math-Ph], December 31, 2015. http://ar
  2 KB (333 단어) - 2020년 11월 13일 (금) 07:38
• Finite dimensional representations of Sl(2)
  [[분류:Lie theory]]
  615 바이트 (51 단어) - 2020년 12월 28일 (월) 05:21
• Vector valued differential forms
  ==exercise from Chern-Simons theory== * [[Chern-Simons gauge theory and invariant|Chern-Simons invariant]]
  2 KB (267 단어) - 2021년 2월 17일 (수) 02:40
• BGG reciprocity
  [[분류:Lie theory]]
  648 바이트 (67 단어) - 2020년 11월 13일 (금) 07:51
• Heisenberg group and Heisenberg algebra
  ...entral extension of groups and Lie algebras|central extension]] of abelian Lie algebra * define a Lie bracket<math>[d,x]=d(x)</math>
  4 KB (568 단어) - 2021년 2월 17일 (수) 03:13
• Baum-Connes conjecture
  ...dentifying the K-theory of a group C∗-algebra, be it a discrete group or a Lie group (or the C∗-algebra of a foliation), and a topological group of equi
  553 바이트 (70 단어) - 2021년 2월 17일 (수) 02:17
• Miura transform for W-algebra
  * Bouwknegt, P., and K. Schoutens. “W-Symmetry in Conformal Field Theory.” Physics Reports 223, no. 4 (February 1993): 183–276. doi:10.1016/0370 ..., and Sergei Igonin. “Miura-Type Transformations for Lattice Equations and Lie Group Actions Associated with Darboux-Lax Representations.” arXiv:1512.09
  908 바이트 (90 단어) - 2020년 11월 13일 (금) 10:28
• Affine Kac-Moody algebras as central extensions of loop algebras
  * Construct the loop algebra from a finite dimensional Lie algebra * start with a semisimple Lie algebra <math>\mathfrak{g}</math> with invariant form <math>\langle \cdot,\
  3 KB (492 단어) - 2020년 11월 16일 (월) 11:01
• Gelfand-Tsetlin bases
  * [[Brauer-Weyl-Frobenius-Schur theory]] * Molev, A. I. 2002. “Gelfand-Tsetlin Bases for Classical Lie Algebras”. ArXiv e-print math/0211289. http://arxiv.org/abs/math/0211289.
  3 KB (388 단어) - 2021년 2월 17일 (수) 03:03
• 군의 작용
  ...hism.<ref name="ref_a94b01fa">[https://www.mathphysicsbook.com/mathematics/lie-groups/representations/group-actions/ Mathematics for Physics]</ref> ...mooth homomorphism from a Lie group \({G}\) to \({\textrm{Diff}(M)}\), the Lie group of diffeomorphisms of a manifold \({M}\).<ref name="ref_a94b01fa" />
  4 KB (616 단어) - 2021년 2월 17일 (수) 00:51
• Infinite Wedge Representation and BLOCH-OKOUNKOV CORRELATION FUNCTIONS
  [[분류:Lie theory]]
  922 바이트 (107 단어) - 2020년 11월 13일 (금) 21:17
• Poincare group and Poincare algebra
  [[분류:Lie theory]]
  1,009 바이트 (114 단어) - 2021년 2월 17일 (수) 02:34
• Representation theory of real reductive groups
  * [[Atlas of Lie Groups and Representations project]] * David A. Vogan, Jr. Irreducible characters of semisimple Lie groups IV. character-multiplicity duality
  3 KB (498 단어) - 2020년 11월 14일 (토) 01:27
• Quantized coordinate ring
  * <math>\mathfrak{g}</math> : simple Lie algebra over <math>\mathbb{C}</math> * <math>G</math> : connected, simply-connected simple algebraic group with Lie algebra <math>\mathfrak{g}</math>
  3 KB (445 단어) - 2020년 11월 13일 (금) 18:57
• Kazhdan-Lusztig conjecture
  ...ble characters in the BGG category <math>\mathcal{O}</math> of semisimple Lie algebras ([KL], [BB], [BK]). * The theory was originally formulated in terms of the canonical bases (i.e., Kazhdan-Lu
  2 KB (255 단어) - 2021년 2월 17일 (수) 02:07
• Discrete subgroups of Lie groups
  [[분류:Lie theory]]
  847 바이트 (123 단어) - 2020년 11월 13일 (금) 03:09
• Infinite Dimensional Unitary Representations of Lie Groups
  * Schmid, Wilfried, and Kari Vilonen. ‘Hodge Theory and Unitary Representations, in the Example of <math>\mathrm{SL}(2,\mathbb{ ..., Sugiura. ‘The Origins of Infinite Dimensional Unitary Representations of Lie Groups’. In The Intersection of History and Mathematics, edited by Profes
  899 바이트 (104 단어) - 2021년 2월 17일 (수) 03:03
• 트리로그 함수(trilogarithm)
  * Goncharov, A. B. 2000. Geometry of the trilogarithm and the motivic Lie algebra of a field. math/0011168 (November 21). http://arxiv.org/abs/math/0 * The classical trilogarithm, algebraic <math>K</math>-theory of fields, and Dedekind zeta functions
  2 KB (236 단어) - 2020년 12월 28일 (월) 04:03
• Ring of symmetric functions
  S\otimes \mathbb{Q} is UEA of a Lie algebra (2) representation theory of symmetric group S_n
  1 KB (151 단어) - 2021년 2월 17일 (수) 02:41
• Constrained system : U(1) pure gauge theory
  * U(1) pure gauge theory : theory of light (without matter)<math>\mathcal{L}_{\text{free}} = - \frac{1}{4}F_{ * [[no-ghost theorem and the construction of moonshine module and monster Lie algbera]]
  1 KB (197 단어) - 2021년 2월 17일 (수) 02:41
• 매스매티카 패키지 (Mathematica packages)
  ...for Computations in Representation Theory of Finite-dimensional and Affine Lie Algebras.” arXiv:1107.4681 (July 23). doi:10.1016/j.cpc.2012.06.014. http [http://www.numbertheory.org/ntw/N1.html Number theory calculator sites/tables]
  3 KB (353 단어) - 2020년 12월 28일 (월) 03:20
• Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras
  ...Hirota equations relates to the vertex operators from elementary particle theory. ...functions we introduce provide a glipse of the atmosphere of quantum field theory.
  5 KB (740 단어) - 2020년 12월 28일 (월) 05:18
• Loop groups and loop algebras
  * Garland, Howard. 1978. “The Arithmetic Theory of Loop Algebras.” Journal of Algebra 53 (2): 480–551. doi:[http://dx.d [[분류:Lie theory]]
  1 KB (167 단어) - 2021년 2월 17일 (수) 02:07
• 단봉수열 (unimodal sequence)
  ...dal Sequences Arising from Lie Algebras.” In Combinatorics, Representation Theory and Statistical Methods in Groups, 57:127–136. Lecture Notes in Pure and ...B. 1977. “Lie Algebraic Proofs of Some Theorems on Partitions.” In Number Theory and Algebra, 135–155. New York: Academic Press. http://www.ams.org/mathsc
  1 KB (159 단어) - 2020년 11월 16일 (월) 05:24
• 단체 집합
  ...notion of a "well-behaved" topological space for the purposes of homotopy theory.<ref name="ref_8195fb4d" /> ...om/doi/abs/10.1112/topo.12073 Homotopy theory of complete Lie algebras and Lie models of simplicial sets]</ref>
  4 KB (585 단어) - 2021년 2월 17일 (수) 01:00
• BGG resolution
  * see [[Kostant theorem on Lie algebra cohomology of nilpotent subalgebra]] * [[Kostant theorem on Lie algebra cohomology of nilpotent radical]]
  4 KB (591 단어) - 2020년 11월 16일 (월) 05:25
• Cyclotomic numbers and Chebyshev polynomials
  * [[sl(2) - orthogonal polynomials and Lie theory]]
  983 바이트 (118 단어) - 2020년 12월 28일 (월) 05:01
• Zonal spherical function
  # The abstract functional analytic theory of zonal spherical functions was first developed by Roger Godement.<ref nam # For semisimple p-adic Lie groups, the theory of zonal spherical functions and Hecke algebras was first developed by Sata
  5 KB (745 단어) - 2021년 2월 22일 (월) 20:27
• Categorification in mathematics
  ...as been a remarkable success with the representation theory of semi-simple Lie algebras (and their associated quantum groups). * Matsuoka, Takuo. “A Generalization of Categorification, and Higher ‘Theory’ of Algebras.” arXiv:1509.01582 [math], September 7, 2015. http://arxiv
  1 KB (165 단어) - 2020년 11월 13일 (금) 17:40
• Calogero-Moser system
  # The goal of the present lecture notes is to give an introduction to the theory of Calogero–Moser systems, highlighting their interplay with these fields ..., and more specifically Calogero-Moser systems, Cherednik algebras and the theory of Frobenius manifolds.<ref name="ref_20390d6d">[https://gow.epsrc.ukri.org
  3 KB (457 단어) - 2021년 1월 2일 (토) 06:14
• Tensor product decompositions of representations of Lie algebras
  ...tp://mathoverflow.net/questions/85593/decompose-tensor-product-of-type-g-2-lie-algebras ...ranch_rule.pdf A Constructive Algorithm for Determining Branching Rules of Lie Group Representations]
  5 KB (598 단어) - 2020년 11월 13일 (금) 19:36
• Springer correspondence
  ...oup and the geometry of the nilpotent cone of the corresponding semisimple Lie algebra * Given a semisimple algebraic group <math>G</math> with Lie algebra <math>\mathfrak{g}</math>, we call the closure of a <math>G</math>-
  3 KB (432 단어) - 2021년 2월 17일 (수) 02:01
• Kostant theorem on character values at the Coxeter element
  ...torus and yield a single conjugacy class (Coxeter conjugacy class) in the Lie group ...as power series, summing over the irreducible representations of suitable Lie groups.
  8 KB (1,307 단어) - 2020년 11월 13일 (금) 23:39
• 수학 백과사전과 테이블
  ...ster? http://mathoverflow.net/questions/63033/what-would-you-want-on-a-lie-theory-cheat-poster.
  2 KB (166 단어) - 2020년 12월 28일 (월) 03:33
• Quantum Invariants of Knots and 3-Manifolds by Turaev
  ...an abstraction of key properties of 2-dimensional rational conformal field theory. Three-dimensional TQFTs can be described via 2-dimensional modular functor ...alizations of knots and links to a category of shlinks (shadow links). The theory of state sums on shadows yields a proof that the Turaev-Viro invariant (def
  3 KB (413 단어) - 2020년 11월 13일 (금) 06:34
• Verma modules
  ...d the well-known category O to study representations of complex semismiple Lie algebras [BGG2]. * [[Geometric representation theory]]
  6 KB (854 단어) - 2021년 2월 17일 (수) 02:23
• Representations of symmetrizable Kac-Moody algebras
  [[분류:Lie theory]]
  1 KB (214 단어) - 2020년 11월 16일 (월) 11:07
• History of Lie theory
  * Sophus Lie—the precursor of the modern theory of Lie groups ...al concepts and theorems on the structure and classification of semisimple Lie algebras
  17 KB (2,525 단어) - 2021년 2월 17일 (수) 03:03
• Affine Hecke algebra
  ...6279-11-8_26 Affine Hecke Algebras, Cyclotomic Hecke algebras and Clifford Theory]</ref> # One of the central objects of study in Representation Theory is the affine Hecke algebra, because answers to many seemingly unrelated qu
  4 KB (592 단어) - 2021년 2월 17일 (수) 00:45
• Bloch-Beilinson conjecture for elliptic curves
  ...ations of Algebraic <math>K</math>-Theory to Algebraic Geometry and Number Theory, Part I, II (Boulder, Colo., 1983), 55:79–88. Contemp. Math. Providence, ...1987. “Elliptic Curves and Values of <math>L</math>-Functions.” In Number Theory (Montreal, Que., 1985), 7:371–387. CMS Conf. Proc. Providence, RI: Amer.
  4 KB (494 단어) - 2021년 2월 17일 (수) 02:54
• Talk on Chevalley's integral forms
  * Chevalley 1955, integral forms for finite-dimensional simple Lie algebras => construction of Chevalley groups ([[Chevalley integral form]]) * Kostant 1966, integral forms for the UEAs of simple Lie algebras (see [[The fake monster formal group by Borcherds]] for more)
  12 KB (2,107 단어) - 2020년 11월 13일 (금) 20:04
• Affine sl(2)
  ==construction from semisimple Lie algebra== * Let <math>\mathfrak{g}</math> be a semisimple Lie algebra with root system <math>\Phi</math> and the invariant form <math>\la
  10 KB (1,592 단어) - 2020년 12월 28일 (월) 05:24
• Talk on finite-dimensional representations of quantum affine algebras
  * f-dim'l reps of affine Lie algebra * Kac-Moody alg assoc. to <math>A</math> is the Lie alg generated by <math>e_i,f_i ,h_i(i\in I)</math>, <math>d_j,(j\in\{1,\dot
  11 KB (2,088 단어) - 2020년 11월 13일 (금) 23:14
• Cartan datum
  [[분류:Lie theory]]
  1 KB (261 단어) - 2020년 12월 28일 (월) 05:14
• Current algebra and anomalies in gauge field theory
  * Weinberg, Steven. “Effective Field Theory, Past and Future.” arXiv:0908.1964 [gr-Qc, Physics:hep-Ph, Physics:hep-Th * Sugawara, Hirotaka. ‘A Field Theory of Currents’. Physical Review 170, no. 5 (25 June 1968): 1659–62. doi:1
  3 KB (346 단어) - 2021년 2월 17일 (수) 02:00
• Virasoro algebra
  * representation theory, see [[highest weight representation of Vir]] * Lie algebra of vector fields on the unit circle
  9 KB (1,217 단어) - 2021년 2월 17일 (수) 02:32
• 콕세터 원소(Coxeter element)
  ...nam.mx/jap/articulos/31.pdf Coxeter transformations and the representation theory of algebras] ...aralampos A. Evripidou. “Characteristic and Coxeter Polynomials for Affine Lie Algebras.” arXiv:1409.3956 [math], September 13, 2014. http://arxiv.org/a
  4 KB (473 단어) - 2021년 2월 17일 (수) 06:02
• Categorification
  ...categorification (part of the CRM thematic semester New Directions in Lie Theory).<ref name="ref_f6f3a255" /> # The course will begin with a very brief review of the representation theory of associative algebras, before introducing the concept of weak categorific
  10 KB (1,397 단어) - 2021년 2월 17일 (수) 00:50
• 직교다항식
  .... “An Overview of the Relationship between Group Theory and Representation Theory to the Special Functions in Mathematical Physics.” arXiv:1309.2544 [math- ...u.co/index.php/recolma/article/viewFile/33654/33627 Special functions, Lie theory and partial differential equations], 1997
  4 KB (375 단어) - 2020년 12월 28일 (월) 03:57
• 조합론
  ...s" to refer to a larger subset of discrete mathematics that includes graph theory.<ref name="ref_ecbd2e6f">[https://mathworld.wolfram.com/Combinatorics.html # Combinatorial theory is the name now given to a subject formerly called "combinatorial analysis"
  9 KB (1,223 단어) - 2020년 12월 21일 (월) 07:33
• 3-manifolds and their invariants
  * [[Chern-Simons gauge theory and Witten's invariant]] ** Kauffman and Line 'The Temperley Lie algebra recoupling theory and invariants of 3-manifolds"
  4 KB (506 단어) - 2021년 2월 17일 (수) 02:12
• 칼라비-야우 다양체
  ...such a can be defined globally, and the Lie group is very important in the theory.<ref name="ref_dbbceabb" /> ...arts/science/physics/string-theory-and-calabi-yau-manifolds-178085/ String Theory and Calabi-Yau Manifolds]</ref>
  10 KB (1,506 단어) - 2022년 7월 7일 (목) 04:24
• Integrable perturbations of Ising model
  ** Ising field theory ==Ising field theory==
  8 KB (1,068 단어) - 2020년 11월 16일 (월) 11:06
• 호프 대수(Hopf algebra)
  * '군 (group)' ([[군론(group theory)]] 항목 참조) 개념의 일반화 * simple Lie algebra <math>\mathfrak{g}</math>
  5 KB (667 단어) - 2021년 2월 17일 (수) 03:50
• Virasoro singular vectors
  * Millionschikov, Dmitry. “Singular Virasoro Vectors and Lie Algebra Cohomology.” arXiv:1405.6734 [math], May 26, 2014. http://arxiv.o ...y. “Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras.” Symmetry, Integrability and Geometry: Methods and Applications
  5 KB (800 단어) - 2020년 11월 13일 (금) 08:50
• Talk on Rogers-Ramanujan identities in affine Kac-Moody algebras
  ...educible representation with dominant integral highest weight of an affine Lie algebra can be written as a finite sum of theta functions with coefficients ==review of affine Lie algebras and their integrable representations==
  11 KB (1,820 단어) - 2020년 11월 13일 (금) 19:56
• Sato theory
  ...ons) solve the KP hierarchy and, based on this observation, he created the theory of the infinite-dimensional (universal) Grassmann manifold and showed that * This implies that the affine Lie algebra A(1) 1 is the infinitesimal transformation group for solutions of t
  6 KB (729 단어) - 2020년 12월 28일 (월) 05:07
• Theta functions in affine Kac-Moody algebras
  [[분류:Lie theory]]
  2 KB (421 단어) - 2020년 11월 16일 (월) 05:34
• Differential Galois theory
  * differential galois theory * [[2008년 12월~09년 1월 한국 방문|2008년 12월]] 9일 MCF 'differential Galois theory'
  8 KB (1,106 단어) - 2021년 2월 17일 (수) 03:11
• 실체에 이르는 길(로저 펜로즈)
  ** representation theory of Lie groups and Lie algebras
  4 KB (273 단어) - 2014년 1월 29일 (수) 03:01
• Talk on String functions and quantum affine algebras
  ...educible representation with dominant integral highest weight of an affine Lie algebra can be written as a linear combination of theta functions, with coe ==review of affine Lie algebras and their integrable representations==
  15 KB (2,422 단어) - 2020년 11월 16일 (월) 05:31
• 축구공의 수학
  ...am Kostant, and Shlomo Sternberg. 1994. “Groups and the Buckyball.” In Lie Theory and Geometry, 123:97–126. Progr. Math. Boston, MA: Birkhäuser Boston. ht * James, Gordon. 1994. “The Representation Theory for Buckminsterfullerene.” Journal of Algebra 167 (3): 803–820. doi:10.
  4 KB (336 단어) - 2020년 12월 28일 (월) 03:59
• 각운동량의 양자 이론
  ...Wormer, [http://www.theochem.ru.nl/%7Epwormer/angmom.pdf ANGULAR MOMENTUM THEORY] * [http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/chp5.pdf Theory of Angular Momentum and Spin]
  5 KB (442 단어) - 2020년 11월 16일 (월) 04:56
• 학부생을 위한 읽기 목록
  * [http://www.jstor.org/stable/2324924 Number Theory as Gadfly] * [http://www.jstor.org/stable/2323277 Very Basic Lie Theory]
  7 KB (890 단어) - 2014년 5월 26일 (월) 16:34
• 공대수 (coalgebra)
  ...bout/Lie_theory_and_special_functions.html?id=XJ9RiMLiOigC&redir_esc=y Lie Theory and Special Functions]. Academic Press. ..._Theory_of_Grou.html?id=08hPoGgSQFIC&redir_esc=y Special Functions and the Theory of Group Representations]. American Mathematical Soc.
  5 KB (579 단어) - 2020년 11월 13일 (금) 09:36
• Vertex operator algebra (VOA)
  * Jacobi identity for Lie algebra says<math>(\operatorname{ad} u)(\operatorname{ad} v)-(\operatorname * Gilroy, Thomas, and Michael P. Tuite. “Genus Two Zhu Theory for Vertex Operator Algebras.” arXiv:1511.07664 [hep-Th], November 24, 20
  3 KB (438 단어) - 2021년 2월 17일 (수) 02:15
• 셀베르그 적분(Selberg integral)
  * Conformal field theory (KZ equations) * Gauge theory (supersymmetry, AGT conjecture)
  5 KB (565 단어) - 2021년 2월 17일 (수) 05:48
• 몬스터 군
  * 유한단순군의 분류결과, 대부분의 유한단순군은 리(Lie) 타입에 속하며 (리타입 외에도 순환군과 교대군이 있음) ** [[군론(group theory)|군론]]
  4 KB (368 단어) - 2021년 2월 17일 (수) 05:42
• Chern-Simons gauge theory and Witten's invariant
  * prototypical example of [[Topological quantum field theory(TQFT)]] * Witten introduced classical Chern-Simons theory to topology
  9 KB (1,284 단어) - 2021년 2월 17일 (수) 02:54
• Monoidal categorifications of cluster algebras
  * Leclerc, 2012, Cluster algebras and Lie theory, http://www.emis.de/journals/SLC/wpapers/s69vortrag/leclerc.pdf
  4 KB (503 단어) - 2020년 11월 14일 (토) 02:54
• Yang-Baxter equation (YBE)
  * in 1+1D S-matrix theory, the YBE is the condition for consistent factorization of the multiparticle ...tation of the [[Braid group]], which then gives a link invariant in [[Knot theory]]
  7 KB (880 단어) - 2021년 2월 17일 (수) 02:28
• Appell-Lerch sums
  ...of representations in (nonrational) conformal field theory models based on Lie superalgebras\ ...ell [http://www.jstor.org/stable/1969153 On a Function Which Occurs in the Theory of the Structure of Polymers], The Annals of Mathematics, Second Series, Vo
  5 KB (852 단어) - 2020년 11월 13일 (금) 09:49
• 데데킨트 제타함수
  ...lois theory, algebraic number theory and zeta functions" ,in \ From number theory to physics", ed. M. Walschmidt, P. Moussa, J.-M. Luck, C. Itzykson Springer * H. M. Stark, The analytic theory of algebraic numbers http://projecteuclid.org/DPubS?service=UI&version=1.0&
  8 KB (1,089 단어) - 2021년 2월 26일 (금) 02:41
• 로지스틱 사상
  ...f0f5058">[https://geoffboeing.com/2015/03/chaos-theory-logistic-map/ Chaos Theory and the Logistic Map]</ref> # As is often the case in dynamical systems theory, the action of the logistic map can not only be represented algebraically,
  8 KB (1,326 단어) - 2021년 2월 26일 (금) 02:01
• 콕세터 군의 푸앵카레 급수
  * Bott, Raoul. “An Application of the Morse Theory to the Topology of Lie-Groups.” Bulletin de La Société Mathématique de France 84 (1956): 251�
  4 KB (441 단어) - 2020년 11월 12일 (목) 22:54
• Talk on BGG resolution
  * standard resolution of trivial module in [[Lie algebra cohomology]] ** see Knapp, Lie Groups, Lie Algebras, and Cohomology IV.6
  22 KB (3,854 단어) - 2020년 11월 14일 (토) 02:14
• 디오판투스 방정식
  ...to a Diophantine equation is closely tied to modular arithmetic and number theory.<ref name="ref_bbcbc179">[https://artofproblemsolving.com/wiki/index.php/Di # The solutions to the diophantine equation correspond to lattice points that lie on the line.<ref name="ref_bbcbc179" />
  6 KB (763 단어) - 2021년 2월 17일 (수) 05:03
• Jacobi's theta function from a representation theoretic viewpoint
  * Jacobi introduced his theta functions to develop the theory of elliptic functions. Weil's approach to theta functions opened up the way * the Lie algebra <math>\mathfrak{h}(2g,\mathbb{R})</math> of <math>H(2g,\mathbb{R})<
  15 KB (2,645 단어) - 2020년 11월 16일 (월) 05:31
• Hecke indefinite modular forms
  ...olt-Raum, Martin. “H-Harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Indefinite Theta Series.” arXiv:1207.5603 [math], July 24, 2012. http: * Kac, V. G., and D. H. Peterson. ‘Affine Lie Algebras and Hecke Modular Forms’. Bulletin (New Series) of the American
  5 KB (726 단어) - 2020년 11월 16일 (월) 05:33
• 추상대수학
  * [[군론(group theory)|군론]] * [[#|체론(field theory)]]
  13 KB (1,574 단어) - 2021년 2월 17일 (수) 06:01
• E8 루트 시스템
  * Borcherds' lectures on Lie groups from [http://math.berkeley.edu/%7Eanton/index.php?m1=writings Anton' .../math.ucr.edu/home/baez/kostant/ On Some Mathematics in Garrett Lisi's 'E8 Theory of Everything']
  16 KB (1,155 단어) - 2021년 2월 17일 (수) 04:47
• Kazhdan-Lusztig polynomial
  * KL polys have applications to the representation theory of semisimple algebraic groups, Verma modules, algebraic geometry and topol * [[Affine Lie algebras at the critical level]]
  6 KB (849 단어) - 2021년 2월 17일 (수) 03:10
• 선형계획법
  # Future possibilities lie in finding LP solutions for diets by combining nutritional, costs, ecologic # Linear programming theory falls within convex optimization theory and is also considered to be an important part of operations research.<ref
  15 KB (2,290 단어) - 2021년 2월 17일 (수) 00:56
• Lectures on dilogarithm function
  ===algebraic K-theory=== ...iangle with vertices <math>0,1,e^{2\pi i/3}</math> translated so that they lie on the circle with center <math>(0,0)</math>
  15 KB (2,512 단어) - 2020년 12월 28일 (월) 05:07
• 다양체
  * For example, all "cat images" might lie on a lower-dimensional manifold compared to say their original 256x256x3 im * with pages giving succinct and precise of important concepts in the theory of manifolds.<ref name="ref_f26f">[http://www.map.mpim-bonn.mpg.de/ Manifol
  9 KB (1,378 단어) - 2020년 12월 16일 (수) 12:00
• Great Mathematics Books of the Twentieth Century by Ji
  * Abikoff The Real Analytic Theory of Teichmüller Space, 136 * Abramenko, Brown Buildings. Theory and Applications, 455
  55 KB (6,316 단어) - 2020년 11월 16일 (월) 05:35
• 다중 제타 값
  * Schneps, Leila. ‘ARI, GARI, Zig and Zag: An Introduction to Ecalle’s Theory of Multiple Zeta Values’. arXiv:1507.01534 [math], 6 July 2015. http://ar ...hs.bris.ac.uk/events/meetings/uploads/4159LeilaSchnepsII.pdf Survey of the theory of multiple zeta values], Leila Schneps
  23 KB (3,134 단어) - 2021년 7월 4일 (일) 19:42
• 구면조화함수(spherical harmonics)
  ...p://staff.science.uva.nl/~thk/art/sheets/DigitalAge.pdf Algebraic methods: Lie groups, quantum groups] # Many aspects of the theory of Fourier series could be generalized by taking expansions in spherical ha
  23 KB (3,277 단어) - 2021년 2월 22일 (월) 20:46
• 미적분학
  # Calculating curves and areas under curves The roots of calculus lie in some of the oldest geometry problems on record.<ref name="ref_8519160f"> ...ted in two chapters, the differential calculus in Chapter 3, and the basic theory of ordinary differential equations in Chapter 6.<ref name="ref_a613b142" />
  15 KB (2,214 단어) - 2021년 2월 23일 (화) 03:29
• 벤포드의 법칙
  * Manack, Corey, and Steven J. Miller. ‘Leading Digit Laws on Linear Lie Groups’. arXiv:1507.01605 [math], 6 July 2015. http://arxiv.org/abs/1507. ...e="ref_3429ddfb">[https://www.jstor.org/stable/j.ctt1dr358t Benford's Law: Theory and Applications on JSTOR]</ref>
  23 KB (2,134 단어) - 2021년 2월 12일 (금) 09:40
• 기존 스프링노트에서의 전체 문서 목록
  *** [[군론(group theory)]] **** [[리만 곡면에서의 호지 이론(Hodge theory)]]
  39 KB (958 단어) - 2014년 1월 1일 (수) 17:26