Zappa–Szép products of semigroups and their C*-algebras

Brownlowe, N., Ramagge, J., Robertson, D. and Whittaker, M. (2014) Zappa–Szép products of semigroups and their C*-algebras. Journal of Functional Analysis, 266(6), pp. 3937-3967. (doi:10.1016/j.jfa.2013.12.025)

Brownlowe, N., Ramagge, J., Robertson, D. and Whittaker, M. (2014) Zappa–Szép products of semigroups and their C*-algebras. Journal of Functional Analysis, 266(6), pp. 3937-3967. (doi:10.1016/j.jfa.2013.12.025)

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Abstract

Zappa–Szép products of semigroups provide a rich class of examples of semigroups that include the self-similar group actions of Nekrashevych. We use Li's construction of semigroup C*-algebras to associate a C*-algebra to Zappa–Szép products and give an explicit presentation of the algebra. We then define a quotient C*-algebra that generalises the Cuntz–Pimsner algebras for self-similar actions. We indicate how known examples, previously viewed as distinct classes, fit into our unifying framework. We specifically discuss the Baumslag–Solitar groups, the binary adding machine, the semigroup N⋊N×, and the ax+b-semigroup Z⋊Z×.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Whittaker, Dr Michael
Authors: Brownlowe, N., Ramagge, J., Robertson, D., and Whittaker, M.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Functional Analysis
Publisher:Elsevier
ISSN:0022-1236
ISSN (Online):1096-0783

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