Homology and Twisted C*-Algebras for Self-similar Actions and Zappa–Szép Products
| dc.contributor.author | Mundey, A. | |
| dc.contributor.author | Sims, A. | |
| dc.date.issued | 2025 | |
| dc.description.abstract | We study the categorical homology of Zappa–Szép products of small categories, which include all self-similar actions. We prove that the categorical homology coincides with the homology of a double complex, and so can be computed via a spectral sequence involving homology groups of the constituent categories. We give explicit formulae for the isomorphisms involved, and compute the homology of a class of examples that generalise odometers. We define the C* -algebras of self-similar groupoid actions on k-graphs twisted by 2-cocycles arising from this homology theory, and prove some fundamental results about their structure. | |
| dc.description.statementofresponsibility | Alexander Mundey, and Aidan Sims | |
| dc.identifier.citation | Results in Mathematics, 2025; 80(1):9-1-9-72 | |
| dc.identifier.doi | 10.1007/s00025-024-02264-7 | |
| dc.identifier.issn | 1422-6383 | |
| dc.identifier.issn | 1420-9012 | |
| dc.identifier.orcid | Mundey, A. [0000-0002-7791-4383] | |
| dc.identifier.uri | https://hdl.handle.net/2440/147801 | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP220101631 | |
| dc.rights | © 2024 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
| dc.source.uri | https://doi.org/10.1007/s00025-024-02264-7 | |
| dc.subject | Self-similar action; Zappa–Szép product; homology; twisted C*-algebra; k-graph. | |
| dc.title | Homology and Twisted C*-Algebras for Self-similar Actions and Zappa–Szép Products | |
| dc.type | Journal article | |
| pubs.publication-status | Published |