1Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE, Scotland, UK 2Institut für Mathematik Universität Paderborn D-33095 Paderborn, Germany
Studia Mathematica, Tome 175 (2006) no. 2, pp. 103-120
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.
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
Affiliations des auteurs :
Robert J. Archbold
1
;
Eberhard Kaniuth
2
1
Department of Mathematical Sciences University of Aberdeen Aberdeen AB24 3UE, Scotland, UK
2
Institut für Mathematik Universität Paderborn D-33095 Paderborn, Germany
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author = {Robert J. Archbold and Eberhard Kaniuth},
title = {Stable rank and real rank of
compact transformation group $C^\ast$-algebras},
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language = {en},
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AU - Eberhard Kaniuth
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Robert J. Archbold; Eberhard Kaniuth. Stable rank and real rank of
compact transformation group $C^\ast$-algebras. Studia Mathematica, Tome 175 (2006) no. 2, pp. 103-120. doi: 10.4064/sm175-2-1
