Lectures on tensor categories and modular functor
imported>Pythagoras0님의 2014년 10월 6일 (월) 19:06 판
introduction
- Bojko Bakalov and Alexander Kirillov, Jr.
examples of modular tensor category
- the category \(\mathcal{C}^{\rm int}(\mathfrak{g},\mathfrak{K})\) of representations of a quantum group
- \(\mathcal{O}_{k}^{\rm int}\) the category of integrable modules of level k over the affine Lie algebra \(\hat{\mathfrak{g}}\)
main results
- thm 7.0.1
The category $\mathcal{O}_{k}^{\rm int}$ has a structure of a modular tensor category.
- thm 7.0.2
The category $\mathcal{O}_{k}^{\rm int}$ is eqiuvalent to the category $\mathcal{C}^{\rm int}(\mathfrak{g},\mathfrak{K})$ as a modular tensor category for $\mathfrak{K}=k+h^{\vee}$, where $h^{\vee}$ is the dual Coxeter number for $\mathfrak{g}$
memo
- http://mathoverflow.net/questions/163708/geometric-intuition-of-p-in-modular-tensor-categories
- Lectures on tensor categories and modular functor
- https://docs.google.com/file/d/0B8XXo8Tve1cxTlhQNm1nU05CakE/edit
articles
- Finkelberg, M. “An Equivalence of Fusion Categories.” Geometric and Functional Analysis 6, no. 2 (1996): 249–67. doi:10.1007/BF02247887.
- Andersen, Henning Haahr, and Jan Paradowski. 1995. “Fusion Categories Arising from Semisimple Lie Algebras.” Communications in Mathematical Physics 169 (3) (May 1): 563–588. doi:10.1007/BF02099312.