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Zappa-Szep products of semigroups and their C*-algebras

By Nathan D Brownlowe, Jacqueline Ramagge, David I Robertson and Michael F Whittaker

Abstract

Zappa-Szep products of semigroups provide a rich class of examples of semigroups that include the self-similar group actions of Nekrashevych. We use Li\u27s construction of semigroups C*-algebras to associate a C*-algebra to Zappa-Szep 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 knowne examples, previously viewed as distinct classes, fit into our unifying framework. We specifically discuss the Baumslag-Solitar groups, the binary adding machine, the semigroup NXNx, and the ax+b semigroup ZXZx

Topics: c, their, semigroups, products, p, sz, zappa, algebras, Engineering, Science and Technology Studies
Publisher: 'Sociological Research Online'
Year: 2014
OAI identifier: oai:ro.uow.edu.au:eispapers-2959
Provided by: Research Online
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