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K-Theory for Semigroup C*-Algebras and Partial Crossed Products
- Source :
- Communications in Mathematical Physics
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Using the Baum-Connes conjecture with coefficients, we develop a K-theory formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups, or equivalently, for certain reduced partial crossed products. In the case of semigroup C*-algebras, we obtain a generalization of previous K-theory results of Cuntz, Echterhoff and the author without having to assume the Toeplitz condition. As applications, we discuss semigroup C*-algebras of Artin monoids, Baumslag-Solitar monoids, one-relator monoids, C*-algebras generated by right regular representations of semigroups from number theory, and C*-algebras of inverse semigroups arising in the context of tilings.<br />24 pages
- Subjects :
- Pure mathematics
Class (set theory)
Conjecture
Mathematics::Operator Algebras
Semigroup
010102 general mathematics
Mathematics - Operator Algebras
Complex system
Inverse
K-Theory and Homology (math.KT)
Statistical and Nonlinear Physics
K-theory
01 natural sciences
Primary 46L80, 46L05, Secondary 20M18, 20Mxx
Mathematics - K-Theory and Homology
0103 physical sciences
FOS: Mathematics
010307 mathematical physics
0101 mathematics
Operator Algebras (math.OA)
Mathematical Physics
Mathematics
Subjects
Details
- ISSN :
- 14320916 and 00103616
- Volume :
- 390
- Database :
- OpenAIRE
- Journal :
- Communications in Mathematical Physics
- Accession number :
- edsair.doi.dedup.....c40d93072fa0788691d4472745047c19