Actions of tensor categories on Kirchberg algebras

2024/05/28 by Kitamura, Kan · 2 citations
#18D25 #46L37 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary 18M40 #Quantum Algebra (math.QA) #Secondary 46L80

paper · doi:10.48550/arxiv.2405.18429

Abstract

We characterize the simplicity of Pimsner algebras for non-proper C*-correspondences. With the aid of this criterion, we give a systematic strategy to produce outer actions of unitary tensor categories on Kirchberg algebras. In particular, every countable unitary tensor category admits an outer action on the Cuntz algebra O₂. We also study the realizability of modules over fusion rings as K-groups of Kirchberg algebras acted on by unitary tensor categories, which turns out to be generically true for every unitary fusion category. Several new examples are provided, among which actions on Cuntz algebras of 3-cocycle twists of cyclic groups are constructed for all possible 3-cohomological classes, thereby answering a question asked by Izumi.

Cited by

• Properly Outer Actions of Tensor Categories on C^*-algebras
• Ergodic automorphisms on Kirchberg algebras

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