Asymptotic K-Theory for Groups Acting on à 2 Buildings

Robertson, Guyan ; Steger, Tim

Canadian journal of mathematics, Tome 53 (2001) no. 4, pp. 809-833

Résumé

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.

Détail

DOI : 10.4153/CJM-2001-033-4

Mots-clés : 46L80, 51E24, K-theory, C*-algebra, affine building

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