k图上的自相似群类群作用和k-论对环同伦的不变性

IF 1 3区数学 Q1 MATHEMATICS

Annals of Functional Analysis Pub Date : 2025-06-17 DOI:10.1007/s43034-025-00440-6

Alexander Mundey, Aidan Sims

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引用次数: 0

摘要

我们建立了有限对准左消去小范畴的包含诱导扭曲\(C^*\) -代数包含的条件。我们也给出了一个包含有限列左消半群的例子，即使在（未扭曲的）Toeplitz代数之间也不会诱导同态。证明了无源行有限k图上可数离散可服从群的联合忠实自相似作用的扭曲\(C^*\) -代数在同伦环下具有同构k理论。

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

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.

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来源期刊

Annals of Functional Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

10.00%

发文量

期刊介绍： Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory. Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.