An Elliott intertwining approach to classifying actions of C^*-tensor categories

2023/10/27 by Sergio Girón Pacheco, Pacheco, Sergio Girón, Robert Neagu +1 · 1 citation
Mathematics · #18D10 #46L35 #46L37 #46L55 #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2310.18125

openalex publication_date 2023/10/27 · openalex created_date 2023/11/01 · openalex updated_date 2026/07/28

Abstract

We introduce a categorical approach to classifying actions of C^*-tensor categories C on C^*-algebras up to cocycle conjugacy. We show that, in this category, inductive limits exist and there is a natural notion of approximate unitary equivalence. Then, we generalise classical Elliott intertwining results to the C-equivariant case, in the same fashion as done by Szabó for the group equivariant case in [39].

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