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The fusion algebra of bimodule categories

Jurgen Fuchs·Ingo Runkel·Christoph Schweigert
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Abstract

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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Jurgen Fuchs, Ingo Runkel, Christoph Schweigert. 2007-01-08. The fusion algebra of bimodule categories. https://doi.org/10.1007/s10485-007-9102-7

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