K-theory for semigroup C*-algebras and partial crossed products

Li, X. (2022) K-theory for semigroup C*-algebras and partial crossed products. Communications in Mathematical Physics, 390(1), pp. 1-32. (doi: 10.1007/s00220-021-04194-9)

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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.

Item Type:Articles
Additional Information:This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817597).
Glasgow Author(s) Enlighten ID:Li, Professor Xin
Authors: Li, X.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
ISSN (Online):1432-0916
Published Online:22 August 2021
Copyright Holders:Copyright © 2021 The Author
First Published:First published in Communications in Mathematical Physics 390(1): 1-32
Publisher Policy:Reproduced under a Creative Commons License
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