Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword affine building

 Expand all        Collapse all Results 1 - 1 of 1

1. CJM 2001 (vol 53 pp. 809)

Robertson, Guyan; Steger, Tim
 Asymptotic $K$-Theory for Groups Acting on $\tA_2$ Buildings Let $\Gamma$ be a torsion free lattice in $G=\PGL(3, \mathbb{F})$ where $\mathbb{F}$ is a nonarchimedean local field. Then $\Gamma$ acts freely on the affine Bruhat-Tits building $\mathcal{B}$ of $G$ and there is an induced action on the boundary $\Omega$ of $\mathcal{B}$. The crossed product $C^*$-algebra $\mathcal{A}(\Gamma)=C(\Omega) \rtimes \Gamma$ depends only on $\Gamma$ and is classified by its $K$-theory. This article shows how to compute the $K$-theory of $\mathcal{A}(\Gamma)$ and of the larger class of rank two Cuntz-Krieger algebras. Keywords:$K$-theory, $C^*$-algebra, affine buildingCategories:46L80, 51E24

© Canadian Mathematical Society, 2014 : https://cms.math.ca/