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Mathematics > Operator Algebras

arXiv:2411.09939 (math)
[Submitted on 15 Nov 2024]

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

Authors:Alexander Mundey, Aidan Sims
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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.
Comments: 18 pages
Subjects: Operator Algebras (math.OA); K-Theory and Homology (math.KT)
MSC classes: 46L05, 46L80 (primary), 20F65 (secondary)
Cite as: arXiv:2411.09939 [math.OA]
  (or arXiv:2411.09939v1 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.2411.09939

Submission history

From: Alexander Mundey [view email]
[v1] Fri, 15 Nov 2024 04:23:33 UTC (25 KB)
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