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Asymptotic K-Theory for Groups Acting on Ã2 Buildings

Published online by Cambridge University Press:  20 November 2018

Guyan Robertson  and
Tim Steger
Guyan Robertson
Affiliation:
Mathematics Department, University of Newcastle, Callaghan, NSW, 2308 Australia e-mail: guyan@maths.newcastle.edu.au
Tim Steger
Affiliation:
Istituto Di Matematica e Fisica, Università degli Studi di, Sassari, Via Vienna 2, 07100 Sassari, Italia e-mail: steger@ssmain.uniss.it
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Abstract

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Let $\Gamma$ be a torsion free lattice in $G=\text{PGL}\left( 3,\mathbb{F} \right)$ where $\mathbb{F}$ is a nonarchimedean local field. Then $\Gamma$ acts freely on the affine Bruhat-Tits building $B$ of $G$ and there is an induced action on the boundary $\Omega$ of $B$. The crossed product ${{C}^{*}}$ -algebra $\mathcal{A}\left( \Gamma \right)=C\left( \Omega \right)\rtimes \Gamma$ depends only on $\Gamma$ and is classified by its $K$-theory. This article shows how to compute the $K$-theory of $\mathcal{A}\left( \Gamma \right)$ and of the larger class of rank two Cuntz-Krieger algebras.

Keywords

46L8051E24K-theoryC*-algebraaffine building
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 53 , Issue 4 , 01 August 2001 , pp. 809 - 833
Copyright
Copyright © Canadian Mathematical Society 2001

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