### 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 |
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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

Archbold, R. J., & Kaniuth, E. (2006). Stable rank and real rank of compact transformation group C*-algebras.

*Studia Mathematica*,*175*(2), 103-120.