The fusion algebra of bimodule categories

Details The fusion algebra of bimodule categories The fusion algebra of bimodule categories

2007-01-08

arxiv.org/abs/math/0701223v1

Appl. Cat. Str. 16 (2008) 123-140

Mathematics

Category Theory

16 pages

Scientific paper

10.1007/s10485-007-9102-7

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.

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