Work

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

Year: 2025

Type: article

Abstract: We establish conditions under which an inclusion of finitely aligned left-cancellative small categories induces inclusions of twisted $$C^*$$ 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 $$C^*$$ 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.

Source: Annals of Functional Analysis

DOI: 10.1007/s43034-025-00440-6

Authors: Alexander Mundey, Aidan Sims

Institution: University of Wollongong

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: University of Wollongong, Australian Research Council