2024 C-ALGEBRAS OF HIGHER-RANK GRAPHS FROM GROUPS ACTING ON BUILDINGS, AND EXPLICIT COMPUTATION OF THEIR K-THEORY
Sam A. Mutter, Aura-Cristiana Radu, Alina Vdovina
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Publ. Mat. 68(1): 187-217 (2024). DOI: 10.5565/PUBLMAT6812408

Abstract

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 k3, which is not a direct consequence of the Künneth theorem for tensor products.

Acknowledgements

The authors would like to thank David Evans and Gwion Evans for discussing the connections between the theory of buildings, higher-rank graphs, and the K-theory of their corresponding C-algebras at the Newton Institute, Cambridge, in spring 2017.

The authors express their gratitude to Newcastle University for providing an excellent research environment, and to the EPSRC for funding part of this research.

Citation

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Sam A. Mutter. Aura-Cristiana Radu. Alina Vdovina. "C-ALGEBRAS OF HIGHER-RANK GRAPHS FROM GROUPS ACTING ON BUILDINGS, AND EXPLICIT COMPUTATION OF THEIR K-THEORY." Publ. Mat. 68 (1) 187 - 217, 2024. https://doi.org/10.5565/PUBLMAT6812408

Information

Received: 17 January 2022; Accepted: 21 June 2023; Published: 2024
First available in Project Euclid: 25 December 2023

MathSciNet: MR4682728
Digital Object Identifier: 10.5565/PUBLMAT6812408

Subjects:
Primary: 19M05

Keywords: buildings , Graph Algebras , higher-rank graphs , ‎K-theory

Rights: Copyright © 2024 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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