Transformation Groups

, Volume 8, Issue 2, pp 177–206 | Cite as

Module categories, weak Hopf algebras and modular invariants

Article

Abstract

We develop a theory of module categories over monoidal categories (this is a straightforward categorization 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 we classify module categories over the fusion category of sl(2) at a positive integer level where we meet once again the ADE classification pattern.

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Copyright information

© Birkhauser Boston 2003

Authors and Affiliations

  1. 1.Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139USA

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