Stable rank and real rank of compact transformation group $C^\ast$-algebras

Robert J. Archbold¹ ; Eberhard Kaniuth²

¹ Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE, Scotland, UK
² Institut für Mathematik Universität Paderborn D-33095 Paderborn, Germany

Studia Mathematica, Tome 175 (2006) no. 2, pp. 103-120

Résumé

Let $(G,X)$ be a transformation group, where $X$ is a locally compact Hausdorff space and $G$ is a compact group. We investigate the stable rank and the real rank of the transformation group $C^\ast$-algebra $C_0(X)\rtimes G$. Explicit formulae are given in the case where $X$ and $G$ are second countable and $X$ is locally of finite $G$-orbit type. As a consequence, we calculate the ranks of the group $C^\ast$-algebra $C^\ast(\mathbb{R}^n \rtimes G)$, where $G$ is a connected closed subgroup of $\mbox{SO}(n)$ acting on $\mathbb{R}^n$ by rotation.

Détail

DOI : 10.4064/sm175-2-1

Keywords: transformation group where locally compact hausdorff space compact group investigate stable rank real rank transformation group ast algebra rtimes explicit formulae given where second countable locally finite g orbit type consequence calculate ranks group ast algebra ast mathbb rtimes where connected closed subgroup mbox acting mathbb rotation