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

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<h5>introduction</h5>
  
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* <math>V=\bigoplus_{n\in\mathbb{Z}}V_{(n)}</math>
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* <math>\dim V_{(n)} <\infty</math> for <math>n\in \mathbb{Z}</math>
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* <math>\dim V_{(n)}=0</math> for <math>n<<0</math>
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*  vertex operator<br><math>V\to (\operatorname{End})[[x,x^{-1}]]</math><br><math>v\mapsto Y(v,x)=\sum</math><br><math>Y(\omega,z)=L(z)=\sum L(n)z^{-n-2}</math><br>
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*  <math>(V,Y,\mathbf{1},D)</math> with the following axioms
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*  locality<br><math>(z_1-z_2)^N[Y(v_1,z_1),Y(v_2,z_2)]=0</math> for some positive integer N<br>
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*  creativity<br><math>Y(v,z).\mathbf{1}=v+\cdots</math><br>
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*  derivation with<br><math>D.\mathbf{1}=0</math><br>
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*  translation covariance  <br><math>[D, Y(v,z)]=\sum_{n}[D,V_n]z^{-n-1}=\partial Y(v,z)</math><br>
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<h5 style="line-height: 2em; margin: 0px;">Virasoro VOA</h5>
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* <math>V=V(c,0)</math> : a highest weight module for [[Virasoro algebra]]<br>
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** <math>\mathbf{1}\in V</math> is the highest weight vector (vacuum)<br>
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**  central charge <math>c\in \mathbb{C}</math><br>
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** <math>L_{-n}\mathbf{1}=0</math> for <math>n\geq 1</math><br>
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** <math>V(c,0)=M(c,0)/\langle L_{-1}\mathbf{1} \rangle</math><br>
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*  conformal vector<br><math>\omega=L_{-2}.\mathbf{1}</math><br><math>Y(\omega,z)=L(z)=\sum L(n)z^{-n-2}</math><br>
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<h5>history</h5>
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
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<h5>related items</h5>
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia</h5>
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* http://en.wikipedia.org/wiki/
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* http://www.scholarpedia.org/
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* http://eom.springer.de
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* http://www.proofwiki.org/wiki/
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* Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])
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<h5>books</h5>
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* [[2011년 books and articles]]
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* http://library.nu/search?q=
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* http://library.nu/search?q=
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<h5>expositions</h5>
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<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles</h5>
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* http://www.ams.org/mathscinet
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* http://www.zentralblatt-math.org/zmath/en/
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* http://arxiv.org/
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* http://www.pdf-search.org/
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* http://pythagoras0.springnote.com/
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
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* http://dx.doi.org/
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<h5>question and answers(Math Overflow)</h5>
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* http://mathoverflow.net/search?q=
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* http://math.stackexchange.com/search?q=
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* http://physics.stackexchange.com/search?q=
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<h5>blogs</h5>
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*  구글 블로그 검색<br>
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**  http://blogsearch.google.com/blogsearch?q=<br>
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** http://blogsearch.google.com/blogsearch?q=
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* http://ncatlab.org/nlab/show/HomePage
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<h5>experts on the field</h5>
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* http://arxiv.org/
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<h5>links</h5>
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]

2012년 7월 17일 (화) 13:07 판

introduction
  • \(V=\bigoplus_{n\in\mathbb{Z}}V_{(n)}\)
  • \(\dim V_{(n)} <\infty\) for \(n\in \mathbb{Z}\)
  • \(\dim V_{(n)}=0\) for \(n<<0\)
  • vertex operator
    \(V\to (\operatorname{End})[[x,x^{-1}]]\)
    \(v\mapsto Y(v,x)=\sum\)
    \(Y(\omega,z)=L(z)=\sum L(n)z^{-n-2}\)
  •  \((V,Y,\mathbf{1},D)\) with the following axioms
  • locality
    \((z_1-z_2)^N[Y(v_1,z_1),Y(v_2,z_2)]=0\) for some positive integer N
  • creativity
    \(Y(v,z).\mathbf{1}=v+\cdots\)
  • derivation with
    \(D.\mathbf{1}=0\)
  • translation covariance  
    \([D, Y(v,z)]=\sum_{n}[D,V_n]z^{-n-1}=\partial Y(v,z)\)

 

 

Virasoro VOA
  • \(V=V(c,0)\) : a highest weight module for Virasoro algebra
    • \(\mathbf{1}\in V\) is the highest weight vector (vacuum)
    • central charge \(c\in \mathbb{C}\)
    • \(L_{-n}\mathbf{1}=0\) for \(n\geq 1\)
    • \(V(c,0)=M(c,0)/\langle L_{-1}\mathbf{1} \rangle\)
  • conformal vector
    \(\omega=L_{-2}.\mathbf{1}\)
    \(Y(\omega,z)=L(z)=\sum L(n)z^{-n-2}\)

 

 

history

 

 

related items

 

 

encyclopedia

 

 

books

 

 

 

expositions

 

 

articles

 

 

 

question and answers(Math Overflow)

 

 

 

blogs

 

 

experts on the field

 

 

links
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