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THE K-THEORY of the C^∗-ALGEBRAS of 2-RANK GRAPHS ASSOCIATED to COMPLETE BIPARTITE GRAPHS

Lookup NU author(s): Dr Sam Mutter

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.Using a result of Vdovina, we may associate to each complete connected bipartite graph κ a two-dimensional square complex, which we call a tile complex, whose link at each vertex is κ. We regard the tile complex in two different ways, each having a different structure as a 2-rank graph. To each 2-rank graph is associated a universal C∗-algebra, for which we compute the K-theory, thus providing a new infinite collection of 2-rank graph algebras with explicit K-groups. We determine the homology of the tile complexes and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.

Publication metadata

Author(s): Mutter SA

Publication type: Article

Publication status: Published

Journal: Journal of the Australian Mathematical Society

Year: 2022

Volume: 113

Issue: 1

Pages: 119 - 144

Print publication date: 01/08/2022

Online publication date: 25/10/2021

Acceptance date: 11/08/2021

Date deposited: 17/06/2022

ISSN (print): 1446-7887

ISSN (electronic): 1446-8107

Publisher: Cambridge University Press

URL: https://doi.org/10.1017/S1446788721000161

DOI: 10.1017/S1446788721000161

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