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arXiv · 1203.0021

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

Xin Li
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Abstract

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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Xin Li. 2012-05-11. Nuclearity of semigroup C*-algebras and the connection to amenability. https://arxiv.org/abs/1203.0021

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