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

2012/01/23 by Joachim Cuntz, Cuntz, Joachim, Siegfried Echterhoff +3
Mathematics · #11R04 (Secondary) #46L05 #46L80 (Primary) 20Mxx #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:11R04 #msc:20Mxx #msc:46L05 #msc:46L80

paper · pdf · doi:10.48550/arxiv.1201.4680

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

openalex publication_date 2012/01/23 · arxiv created 2013/05/25 · arxiv updated 2013/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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