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

Authors

Nathan D. Brownlowe, University of WollongongFollow
Jacqueline Ramagge, University of WollongongFollow
David I. Robertson, University of WollongongFollow
Michael F. Whittaker, University of WollongongFollow

RIS ID

86560

Publication Details

Brownlowe, N. D., Ramagge, J., Robertson, D. I. & Whittaker, M. F. (2014). Zappa-Szep products of semigroups and their C*-algebras. Journal of Functional Analysis, 266 (6), 3937-3967.

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's 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.

Grant Number

ARC/DP130100490

Additional Grant Number

http://purl.org/au-research/grants/arc/DP130100490