Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912443507146752 |
|---|---|
| author | Mundey, Alexander Sims, Aidan |
| author_facet | Mundey, Alexander Sims, Aidan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies Mundey, Alexander Sims, Aidan Operator Algebras K-Theory and Homology 46L05, 46L80 (primary), 20F65 (secondary) 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. |
| title | Self-similar groupoid actions on k-graphs, and invariance of K-theory for cocycle homotopies |
| topic | Operator Algebras K-Theory and Homology 46L05, 46L80 (primary), 20F65 (secondary) |
| url | https://arxiv.org/abs/2411.09939 |