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Proceedings of the American Mathematical Society

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

 

 

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


Author: Eckart Schulz
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1991-1042272-3
Keywords: $ {{\text{C}}^ * }$-crossed product, stable rank, $ {{\text{C}}^*}$-bundle
Article copyright: © Copyright 1991 American Mathematical Society