Nuclearity of semigroup C*-algebras and the connection to amenability

Details Nuclearity of semigroup C*-algebras and the connection to amenability Nuclearity of semigroup C*-algebras and the connection to amenability

2012-02-29

arxiv.org/abs/1203.0021v1

Mathematics

Operator Algebras

41 pages

Scientific paper

We study C*-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C*-algebras as C*-algebras of inverse semigroups, groupoid C*-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclearity of semigroup C*-algebras in terms of faithfulness of left regular representations and amenability of group actions. Moreover, we also determine when boundary quotients of semigroup C*-algebras are UCT Kirchberg algebras. This leads to a unified approach to Cuntz algebras and ring C*-algebras.

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