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

Volume 175 / 2006

Robert J. Archbold, Eberhard Kaniuth Studia Mathematica 175 (2006), 103-120 MSC: 22D15, 46L35, 54H15. DOI: 10.4064/sm175-2-1

Abstract

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.

Authors

  • Robert J. ArchboldDepartment of Mathematical Sciences
    University of Aberdeen
    Aberdeen AB24 3UE, Scotland, UK
    e-mail
  • Eberhard KaniuthInstitut für Mathematik
    Universität Paderborn
    D-33095 Paderborn, Germany
    e-mail

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