Publication Date:
2013-08-20
Description:
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 α, 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 *( P ) and C *( P ) coincide, although the structure of these algebras can be very different.
Print ISSN:
0033-5606
Electronic ISSN:
1464-3847
Topics:
Mathematics
