K-Theory for Semigroup C-Algebras and Partial Crossed Products

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 a class of reduced partial crossed products. This generalizes and gives a new proof of previous K-theory results of Cuntz, Echt...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 390; no. 1; pp. 1 - 32
Main Author: Li, Xin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Subjects:
Algebra
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Monoids
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Semigroups
Theoretical
ISSN:0010-3616, 1432-0916, 1432-0916
Online Access:Get full text
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Summary: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 a class of reduced partial crossed products. This generalizes and gives a new proof of previous K-theory results of Cuntz, Echterhoff and the author. Our K-theory formula applies to a rich class of C*-algebras which are generated by partial isometries. For instance, as new applications which could not be treated using previous results, we discuss semigroup C*-algebras of Artin monoids, Baumslag-Solitar monoids and one-relator monoids, as well as C*-algebras generated by right regular representations of semigroups of number-theoretic origin, and C*-algebras attached to tilings.
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Communicated by H.-T.Yau
ISSN:0010-3616
1432-0916
1432-0916
DOI:10.1007/s00220-021-04194-9