Module categories, weak Hopf algebras and modular invariants

Details Module categories, weak Hopf algebras and modular invariants Module categories, weak Hopf algebras and modular invariants

2001-11-12

arxiv.org/abs/math/0111139v1

Mathematics

Quantum Algebra

26 pages

Scientific paper

We develop abstract nonsense for module categories over monoidal categories (this is a straightforward categorification of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects is equivalent to the category of representations of a weak Hopf algebra (theorem of T. Hayashi) and classify module categories over the fusion category of $\hat{sl}(2)$ at a positive integer level where we meet once again ADE classification pattern.

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