Browse by author
Lookup NU author(s): Professor Guyan Robertson
Full text for this publication is not currently held within this repository. Alternative links are provided below where available.
Let $\Gamma$ be a torsion free lattice in $G = \PGL(n+1,\FF)$, where $n\ge 1$ and $\FF$ is a non-archimedean local field. Then $\Gamma$ acts on the Furstenberg boundary $G/P$, where $P$ is a minimal parabolic subgroup of $G$. The identity element $\id$ in the crossed product $C^*$-algebra $C(G/P)\rtimes \Gamma$ generates a class $[\id]$ in the $K_0$ group of $C(G/P)\rtimes \Gamma$. It is shown that $[\id]$ is a torsion element of $K_0$ and there is an explicit bound for the order of $[\id]$. The result is proved more generally for groups acting on affine buildings of type $\tA_n$. For $n=1, 2$ the Euler-Poincar\'e characteristic $\chi(\Gamma)$ annihilates the class $[\id]$.
Author(s): Robertson G
Publication type: Article
Publication status: Published
Journal: K-Theory
Year: 2001
Volume: 22
Issue: 3
Pages: 251-269
ISSN (print): 0920-3036
ISSN (electronic): 1573-0514
Publisher: Springer Netherlands
URL: http://dx.doi.org/10.1023/A:1011173718141
DOI: 10.1023/A:1011173718141
Altmetrics provided by Altmetric