ON THE K-THEORY OF CROSSED PRODUCTS BY AUTOMORPHIC SEMIGROUP ACTIONS
ON THE K-THEORY OF CROSSED PRODUCTS BY AUTOMORPHIC SEMIGROUP ACTIONS
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DOI：
10.1093/qmath/hat021
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发表时间：
2013-09-01
影响因子：
0.7
通讯作者：
Li, Xin
中科院分区：
文献类型：
--
作者：
Cuntz, Joachim;Echterhoff, Siegfried;Li, Xin
让P是一个半群,承认一个嵌入到一群G .假设嵌入满足托普利兹条件最近引入的第三作者和Baum-Connes猜想适用于G .我们证明一个公式描述的k理论减少交叉产品(α,r) P P .这个公式得到的任何自同构的行动结果的结果k理论交叉的产品为特殊的行为完全不连通空间的G。将所得结果应用于左半群和拟格有序半群。我们还利用结果表明，对于某些半群P，包括Dedekind定义域R的ax+b半群R-x，左右正则半群C*-代数C-lambda*(P)和C-rho*(P)的k理论是一致的，尽管这些代数的结构可能非常不同。
Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies the Toeplitz condition recently introduced by the third named author and that the Baum-Connes conjecture holds for G. We prove a formula describing the K-theory of the reduced crossed product A(alpha, r)P by any automorphic action of P. This formula is obtained as a consequence of a result on the K-theory of crossed products for special actions of G on totally disconnected spaces. We apply our result to various examples including left Ore semigroups and quasi-lattice ordered semigroups. We also use the results to show that for certain semigroups P, including the ax+b-semigroup R R-x for a Dedekind domain R, the K-theory of the left and right regular semigroup C*-algebras C-lambda*(P) and C-rho*(P) coincide, although the structure of these algebras can be very different.