The Fusion Algebra of Bimodule Categories

We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure of F. As a by-product we obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category in terms of endomorphisms of the tensor unit of the underlying modular tensor category. 

• Type: Journal
• Year: 2008
• Where: ACS
• Authors: Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
• Keywords: ACS 2008, Appropriate Morphism Spaces, Bimodule Categories, Distributed And Parallel Computing, Modular Tensor Category