Hilbert空间上适当等距作用群的紧算子和代数K理论

arXiv: K-Theory and Homology Pub Date : 2013-11-25 DOI:10.1515/CRELLE-2014-0154

Guillermo Cortiñas, Gisela Tartaglia

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引用次数: 1

摘要

我们证明了关于紧算子稳定的系数环和C^*$-代数群的K -理论法雷尔-琼斯猜想。我们利用这一结果和Higson-Kasparov关于带系数的Baum-Connes猜想对这类群成立的结果，证明如果G$如题目所示，那么G$与稳定的C^*$-代数的代数积和C^*$-交叉积具有相同的K$-理论。

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Compact operators and algebraic $K$-theory for groups which act properly and isometrically on Hilbert space

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes conjecture with coefficients holds for such groups, to show that if $G$ is as in the title then the algebraic and the $C^*$-crossed products of $G$ with a stable $C^*$-algebra have the same $K$-theory.

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arXiv: K-Theory and Homology

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