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)

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, Professor Mike
• 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