History of Lie theory
imported>Pythagoras0님의 2013년 12월 6일 (금) 07:59 판
introduction
19세기 프랑스 군론
- 갈루아
- Jordan
- 클라인과 리
리 군
- Sophus Lie—the precursor of the modern theory of Lie groups.
- Wilhelm Killing, who discovered almost all central concepts and theorems on the structure and classification of semisimple Lie algebras.
- Élie Cartan and is primarily concerned with developments that would now be interpreted as representations of Lie algebras, particularly simple and semisimple algebras.
- Hermann Weyl the development of representation theory of Lie groups and algebras.
development of representation theory of Lie groups
- 1913 Cartan spin representations
- 19?? Weyl unitarian trick : Complete reducibility
- Dynkin, The structure of semi-simple Lie algebras
- amre,math.sco.transl.17
on fraktur
- http://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras-mathfrakg-etc
- The point is that group theory and Lie groups in particular were actively developed by German mathematicians in the nineteenth century; they were not inventing exotic notation when they used these particular letters as symbols
리 타입의 유한군
modern development
memo
- history of theory of symmetric polynomials
- the role of invariant theory
articles
- Elie Cartan Sur la structure des groupes de transformations finis et continus Cartan's famous 1894 thesis, cleaning up Killing's work on the classification Lie algebras.
- Wilhelm Killing, "Die Zusammensetzung der stetigen endlichen Transformations-gruppen" 1888-1890 part 1part 2part 3part 4 Killing's classification of simple Lie complex Lie algebras.
- S. Lie, F. Engel "Theorie der transformationsgruppen" 1888 Volume 1Volume 2Volume 3 Lie's monumental summary of his work on Lie groups and algebras.
- Hermann Weyl, Theorie der Darstellung kontinuierlicher halb-einfacher Gruppen durch lineare Transformationen. 1925-1926 I, II, III. Weyl's paper on the representations of compact Lie groups, giving the Weyl character formula.
- H. Weyl The classical groups ISBN 978-0-691-05756-9 A classic, describing the representation theory of lie groups and its relation to invariant theory
- Chevalley, On certain simple groups
표준적인 교과서
- J.-P. Serre, Lie algebras and Lie groups ISBN 978-3540550082 Covers most of the basic theory of Lie algebras.
- J.-P. Serre, Complex semisimple Lie algebras ISBN 978-3-540-67827-4 Covers the classification and representation theory of complex Lie algebras.
- N. Jacobson, Lie algebras ISBN 978-0486638324 A good reference for all proofs about finite dimensional Lie algebras
- Claudio Procesi, Lie Groups: An Approach through Invariants and Representations, ISBN 978-0387260402. Similar to the course, with more emphasis on invariant theory.
expository
- Varadarajan, Historical review of Lie Theory
- Hawkins, Thomas. 1998. “From General Relativity to Group Representations: The Background to Weyl’s Papers of 1925–26.” In Matériaux Pour L’histoire Des Mathématiques Au XX\rm E$ Siècle (Nice, 1996), 3:69–100. Sémin. Congr. Paris: Soc. Math. France. http://www.ams.org/mathscinet-getitem?mr=1640256. http://www.emis.de/journals/SC/1998/3/pdf/smf_sem-cong_3_69-100.pdf
- T. Hawkins Emergence of the theory of Lie groups ISBN 978-0-387-98963-1 Covers the early history of the work by Lie, Killing, Cartan and Weyl, from 1868 to 1926.
- A. Borel Essays in the history of Lie groups and algebraic groups ISBN 978-0-8218-0288-5 Covers the history.
- "From Galois and Lie to Tits Buildings", The Coxeter Legacy: Reflections and Projections (ed. C. Davis and E.W. Ellers), Fields Inst. Publications volume 48, American Math. Soc. (2006), 45–62.