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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The stable rank of crossed products of sectional $C^ *$-algebras by compact Lie groups
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by Eckart Schulz PDF
Proc. Amer. Math. Soc. 112 (1991), 733-744 Request permission

Abstract:

Let $X$ be a second countable, locally compact Hausdorff space, and let a compact Lie group $D$ act on a ${{\text {C}}^ * }$-bundle $(E,X)$, the fibres of which are of bounded, finite dimension. Denote by $A$ the ${{\text {C}}^ * }$-algebra of sections vanishing at infinity, and by $\hat \alpha$ the induced action of $D$ on $A$. The stable ranks of both, the fixed point algebra ${A^{\hat \alpha }}$ and the crossed product algebra $A{ \times _{\hat \alpha }}D$ are determined.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 733-744
  • MSC: Primary 46L55; Secondary 22D25, 46L05
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1042272-3
  • MathSciNet review: 1042272