K-theoretic classification of inductive limit actions of fusion categories on AF-algebras

Abstract

We introduce a K-theoretic invariant for actions of unitary fusion categories on unital C*-algebras. We show that for inductive limits of finite dimensional actions of fusion categories on unital AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on AF-algebras. We apply our results to obtain a classification of finite depth, strongly AF-inclusions of unital AF-algebras.

52 pages, comments welcome!

References in corpus (5)

• Numerical evidence for a Haagerup conformal field theory
• A critical lattice model for a Haagerup conformal field theory
• Q-system completion for C* 2-categories
• Remarks on anomalous symmetries of C*-algebras
• Anyonic Chains -- $\alpha$-Induction -- CFT -- Defects -- Subfactors

Cited by in corpus (6)

• Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility
• Quantum graphs, subfactors and tensor categories I
• The stable uniqueness theorem for unitary tensor category equivariant KK-theory
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable
• A classification of anomalous actions through model action absorption
• Discrete Inclusions of C*-algebras