Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms

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• 作者：Jü ; rgen Fuchs^a ; Christoph Schweigert^b ; ^{christoph.schweigert@uni-hamburg.de} ; Carl Stigner^a
• 关键词：Ribbon Hopf algebra ; Mapping class group
• 刊名：Journal of Algebra
• 出版年：2012
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：1 August, 2012
• 卷：363
• 期：Complete
• 页码：29-72
• 文件大小：979 K

摘要

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism of H, we establish the existence of the following structure: an H-bimodule and a bimodule morphism from Lyubashenko始s Hopf algebra object K for the bimodule category to . This morphism is invariant under the natural action of the mapping class group of the one-punctured torus on the space of bimodule morphisms from K to . We further show that the bimodule can be endowed with a natural structure of a commutative symmetric Frobenius algebra in the monoidal category of H-bimodules, and that it is a special Frobenius algebra iff H is semisimple.

The bimodules K and can both be characterized as coends of suitable bifunctors. The morphism is obtained by applying a monodromy operation to the coproduct of ; a similar construction for the product of exists as well.

Our results are motivated by the quest to understand the bulk state space and the bulk partition function in two-dimensional conformal field theories with chiral algebras that are not necessarily semisimple.