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C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory

Lookup NU author(s): Dr Sam Mutter, Dr Aura-Cristiana Radu, Dr Alina Vdovina

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Abstract

© 2024 Universitat Autonoma de Barcelona. All rights reserved.We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called k-cube groups, which act freely and transitively on the product of k trees, for arbitrary k. The quotient of this action on the product of trees defines a k-dimensional cube complex, which induces a higher-rank graph. We make deductions about the K-theory of the corresponding rank-k graph C*-algebras, and give examples of k-cube groups and their K-theory. These are among the first explicit computations of K-theory for an infinite family of rank-k graphs for k ≥ 3, which is not a direct consequence of the Kunneth theorem for tensor products.

Publication metadata

Author(s): Mutter SA, Radu A-C, Vdovina A

Publication type: Article

Publication status: Published

Journal: Publicacions Matematiques

Year: 2024

Volume: 68

Issue: 1

Pages: 187-217

Print publication date: 01/01/2024

Acceptance date: 21/06/2023

ISSN (print): 0214-1493

ISSN (electronic): 2014-4350

Publisher: Universitat Autonoma de Barcelona

URL: https://doi.org/10.5565/PUBLMAT6812408

DOI: 10.5565/PUBLMAT6812408

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