K-theoretic Classification of Inductive Limit Actions of Fusion Categories on AF-algebras

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 AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit...

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Bibliographic Details
Published in:Communications in mathematical physics 2024-03, Vol.405 (3), Article 83
Main Authors: Chen, Quan, Hernández Palomares, Roberto, Jones, Corey
Format: Article
Language:English
Subjects:
Algebra
Categories
Classical and Quantum Gravitation
Classification
Complex Systems
Group theory
Inclusions
Invariants
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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 AF-algebras, this is a complete invariant. In particular, this gives a complete invariant for inductive limit actions of finite groups on unital AF-algebras. We apply our results to obtain a classification of finite depth, strongly AF-inclusions of unital AF-algebras.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-04969-w