Work

Homology and Twisted $$C^*$$-Algebras for Self-similar Actions and Zappa–Szép Products

Year: 2024

Type: article

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 $$C^*$$ 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.

Source: Results in Mathematics

DOI: 10.1007/s00025-024-02264-7

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: $2,990

Funders: University of Wollongong, Australian Research Council