On the K-theory of the C*-algebra generated by the left regular representation of an Ore semigroup

Abstract

We compute the K-theory of C*-algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the K-theory of these semigroup C*-algebras in terms of the K-theory for the reduced group C*-algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.

44 pages; title has changed; this final version has been accepted for publication in J. Eur. Math. Soc

References in corpus (2)

• K-theory for ring C*-algebras - the case of number fields with higher roots of unity
• C*-algebras of Toeplitz type associated with algebraic number fields

Cited by in corpus (6)

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• Independent resolutions for totally disconnected dynamical systems I: Algebraic case
• On K-theoretic invariants of semigroup C*-algebras attached to number fields
• A new approach to recent constructions of C*-algebras from modular index theory