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arXiv · 2207.11854

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

Quan Chen·Roberto Hernández Palomares·Corey Jones
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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.

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Quan Chen, Roberto Hernández Palomares, Corey Jones. 2022-07-25. K-theoretic classification of inductive limit actions of fusion categories on AF-algebras. https://doi.org/10.1007/s00220-024-04969-w

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