"Vertex operator algebra (VOA)"의 두 판 사이의 차이

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-==definition==
-* vertex operator algbera is a quadruple <math>(V,Y,\mathbf{1},\omega)</math> with the following axioms
-* <math>V=\bigoplus_{n\in\mathbb{Z}}V_{(n)}</math> vector space
-* <math>\dim V_{(n)} <\infty</math> for <math>n\in \mathbb{Z}</math>
-* <math>\dim V_{(n)}=0</math> for <math>n<<0</math>
-*  vertex operator<br><math>V\to (\operatorname{End})[[x,x^{-1}]]</math><br><math>v\mapsto Y(v,x)=\sum_{n\in \mathbb{Z}}v_{n}x^{-n-1}</math><br>
-* two distinguished vectors <math>\mathbf{1}\in V_{(0)}</math> and  <math>\omega\in V_{(2)}</math>
-==vertex algebra vs VOA==
-* grading on V
-==axioms==
-*   <br><math>u_{n}v=0</math> for <math>n>>0</math><br>
-* <math>Y(\mathbf{1},z)=\operatorname{id}_{V}</math>
-*  (creation property)<br><math>Y(v,z).\mathbf{1}=v+\cdots</math><br>
-*  conformal vector<br><math>Y(\omega,z)=L(z)=\sum L(n)z^{-n-2}</math> satisfies<br><math>[L_m,L_n]=(m-n)L_{m+n}+\frac{c}{12}(m^3-m)\delta_{m+n}</math><br>
-* <math>L(0)v=nv</math> for <math>n\in\mathbb{Z}</math> and <math>v\in V_{(n)}</math>
-*  translation covariance  <br><math>[D, Y(v,z)]=\sum_{n}[D,V_n]z^{-n-1}=\partial Y(v,z)</math><br>
-*  Jacobi identity
-:<math>z_0^{-1}\delta(\frac{z_1-z_2}{z_0})Y(u,z_1)Y(v,z_2)-z_0^{-1}\delta(\frac{z_2-z_1}{-z_0})Y(v,z_2)Y(u,z_1)=z_2^{-1}\delta\left(\frac   {z_1-z_0}{z_2}\right)Y(Y(u,z_0)v,z_2)</math>
-==remark on Jacobi identity==
-*  Jacobi identity for Lie algebra says<br><math>(\operatorname{ad} u)(\operatorname{ad} v)-(\operatorname{ad} v)-(\operatorname{ad} u)=(\operatorname{ad}(\operatorname{ad} u) v)</math><br>
-==history==
-* http://www.google.com/search?hl=en&tbs=tl:1&q=
-==related items==
-==expositions==
-* Mason, [http://ws15.amsi.org.au/wp-content/uploads/sites/9/2015/05/Vanderbilt.pdf Vertex Operator Algebras]
-* Mason, [http://ws15.amsi.org.au/wp-content/uploads/sites/9/2015/05/Heidelberg.pdf Vertex Operator Algebras, Modular Forms and Moonshine]
-==articles==
-* Yi-Zhi Huang, Jinwei Yang, Associative algebras for (logarithmic) twisted modules for a vertex operator algebra, arXiv:1603.04367 [math.QA], March 14 2016, http://arxiv.org/abs/1603.04367
-* Gilroy, Thomas, and Michael P. Tuite. “Genus Two Zhu Theory for Vertex Operator Algebras.” arXiv:1511.07664 [hep-Th], November 24, 2015. http://arxiv.org/abs/1511.07664.
-* Ai, Chunrui, and Xingjun Lin. “On the Unitary Structures of Vertex Operator Superalgebras.” arXiv:1510.08609 [math], October 29, 2015. http://arxiv.org/abs/1510.08609.
-* Ding, Lu, Wei Jiang, and Wei Zhang. “Zhu’s Algebra of a C1-Cofinite Vertex Algebra.” arXiv:1508.06351 [math], August 25, 2015. http://arxiv.org/abs/1508.06351.
-* van Ekeren, Jethro, Sven Möller, and Nils R. Scheithauer. “Construction and Classification of Holomorphic Vertex Operator Algebras.” arXiv:1507.08142 [math], July 29, 2015. http://arxiv.org/abs/1507.08142.
-[[분류:개인노트]]

"Vertex operator algebra (VOA)"의 두 판 사이의 차이

2020년 11월 13일 (금) 19:39 판

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