On the K-theory of crossed products by automorphic semigroup actions
arXiv:1205.5412
Abstract
Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies a certain Toeplitz condition and that the Baum-Connes conjecture holds for G. We prove a formula describing the K- theory of the reduced crossed product A \rtimesα,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 for a Dedekind domain R, the K-theory of the left and right regular semigroup C*-algebras of P coincide, although the structure of these algebras can be very different.
References in corpus (6)
- The Regular C*-algebra of an Integral Domain
- C*-algebras associated with endomorphisms and polymorphisms of compact abelian groups
- Nuclearity of semigroup C*-algebras and the connection to amenability
- On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup
- C*-algebras of Toeplitz type associated with algebraic number fields
- Semigroup C*-algebras and amenability of semigroups