Semigroup C⁎-algebras and amenability of semigroups
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We construct reduced and full semigroup C*-algebras for left cancellative semigroups. Our new construction covers particular cases already considered by A. Nica and also Toeplitz algebras attached to rings of integers in number fields due to J. Cuntz. Moreover, we show how (left) amenability of semigroups can be expressed in terms of these semigroup C*-algebras in analogy to the group case.
39 pages; corrected and revised version, new construction added in section 3
- University of Münster Germany
Amenability, 46L05 (Primary) 20Mxx, 43A07 (Secondary), Semigroup, Mathematics - Operator Algebras, FOS: Mathematics, C⁎-algebra, Operator Algebras (math.OA), Analysis
Amenability, 46L05 (Primary) 20Mxx, 43A07 (Secondary), Semigroup, Mathematics - Operator Algebras, FOS: Mathematics, C⁎-algebra, Operator Algebras (math.OA), Analysis
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