Semigroup C*-algebras and amenability of semigroups

Details Semigroup C*-algebras and amenability of semigroups Semigroup C*-algebras and amenability of semigroups

2011-05-27

arxiv.org/abs/1105.5539v2

Mathematics

Operator Algebras

39 pages; corrected and revised version, new construction added in section 3

Scientific paper

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.

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