Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies

2024/11/15 by Alexander Mundey, Mundey, Alexander, Aidan Sims +1 · 1 citation
Mathematics · Physics and Astronomy · #20F65 (secondary) #46L05 #46L80 (primary) #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2411.09939

openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted C*-algebras. We also present an example of an inclusion of finitely aligned left-cancellative monoids that does not induce a homomorphism even between (untwisted) Toeplitz algebras. We prove that the twisted C*-algebras of a jointly faithful self-similar action of a countable discrete amenable groupoid on a row-finite k-graph with no sources, with respect to homotopic cocycles, have isomorphic K-theory.

Cited by

• Lifting isomorphisms in K-theory through gradings of C^*-algebras

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