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

2012/02/29 by Xin Li, Li, Xin · 1 citation
Computer Science · Mathematics · #43A07 #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Primary 46L05 #Secondary 20Mxx

paper · pdf · doi:10.48550/arxiv.1203.0021

openalex publication_date 2012/02/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On K-theoretic invariants of semigroup C*-algebras attached to number fields

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• Nuclearity of semigroup C*-algebras
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