### Abstract

Let (G, X) be a transformation group, where X is a locally compact Hansdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C-o(X) x 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*-algebra C*(R' x G), where G is a connected closed subgroup of SO(n) acting on R-n by rotation.

Original language | English |
---|---|

Pages (from-to) | 103-120 |

Number of pages | 17 |

Journal | Studia Mathematica |

Volume | 175 |

Issue number | 2 |

Publication status | Published - 2006 |

### Keywords

- transformation group
- group C*-algebra
- stable rank
- real rank
- STAR-ALGEBRAS
- CANCELLATION THEOREM
- LIE-GROUPS
- CROSSED-PRODUCTS
- CONTINUOUS TRACE
- MODULES
- ZERO

### Cite this

*Studia Mathematica*,

*175*(2), 103-120.

**Stable rank and real rank of compact transformation group C*-algebras.** / Archbold, Robert J; Kaniuth, E.

Research output: Contribution to journal › Article

*Studia Mathematica*, vol. 175, no. 2, pp. 103-120.

}

TY - JOUR

T1 - Stable rank and real rank of compact transformation group C*-algebras

AU - Archbold, Robert J

AU - Kaniuth, E.

PY - 2006

Y1 - 2006

N2 - Let (G, X) be a transformation group, where X is a locally compact Hansdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C-o(X) x 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*-algebra C*(R' x G), where G is a connected closed subgroup of SO(n) acting on R-n by rotation.

AB - Let (G, X) be a transformation group, where X is a locally compact Hansdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C-o(X) x 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*-algebra C*(R' x G), where G is a connected closed subgroup of SO(n) acting on R-n by rotation.

KW - transformation group

KW - group C-algebra

KW - stable rank

KW - real rank

KW - STAR-ALGEBRAS

KW - CANCELLATION THEOREM

KW - LIE-GROUPS

KW - CROSSED-PRODUCTS

KW - CONTINUOUS TRACE

KW - MODULES

KW - ZERO

M3 - Article

VL - 175

SP - 103

EP - 120

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 2

ER -