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

Robert J Archbold, E. Kaniuth

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)103-120
Number of pages17
JournalStudia Mathematica
Volume175
Issue number2
Publication statusPublished - 2006

Keywords

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

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