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*-algebra C₀(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*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-2-1,
author = {Robert J. Archbold and Eberhard Kaniuth},
title = {Stable rank and real rank of compact transformation group C*-algebras},
journal = {Studia Mathematica},
volume = {173},
year = {2006},
pages = {103-120},
zbl = {1104.22008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-2-1}
}
Robert J. Archbold; Eberhard Kaniuth. Stable rank and real rank of compact transformation group C*-algebras. Studia Mathematica, Tome 173 (2006) pp. 103-120. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm175-2-1/