The fusion algebra of bimodule categories

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.

16 pages

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Cited by in corpus (20)

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• Anomalies and Bounds on Charged Operators
• Tensor categories for vertex operator superalgebra extensions
• Morita classes of algebras in modular tensor categories
• Invertible defects and isomorphisms of rational CFTs
• Topological Defect Lines in Two Dimensional Fermionic CFTs
• Lorentzian Dynamics and Factorization Beyond Rationality
• Perturbed Defects and T-Systems in Conformal Field Theory
• A Defect Verlinde Formula
• Some remarks on defects and T-duality
• Pointed Drinfeld center functor
• On the Symmetries of Classical String Theory
• RCFT with defects: Factorization and fundamental world sheets
• Rigidity and defect actions in Landau-Ginzburg models
• Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Hopf algebras and finite tensor categories in conformal field theory
• A Monoidal Category for Perturbed Defects in Conformal Field Theory
• Module categories for permutation modular invariants
• On representing some lattices as lattices of intermediate subfactors of finite index