The stable rank of crossed products of sectional 𝐶*-algebras by compact Lie groups

Schulz, Eckart

doi:10.1090/S0002-9939-1991-1042272-3

The stable rank of crossed products of sectional $C^ *$-algebras by compact Lie groups
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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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Representations of

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