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

Journal Article


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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 NN×, and the ax + b-semigroup Z Z×.

Publication Date


  • 2014

Citation


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

Scopus Eid


  • 2-s2.0-84893847986

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2959&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1950

Has Global Citation Frequency


Number Of Pages


  • 30

Start Page


  • 3937

End Page


  • 3967

Volume


  • 266

Issue


  • 6

Place Of Publication


  • United States

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 NN×, and the ax + b-semigroup Z Z×.

Publication Date


  • 2014

Citation


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

Scopus Eid


  • 2-s2.0-84893847986

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=2959&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/1950

Has Global Citation Frequency


Number Of Pages


  • 30

Start Page


  • 3937

End Page


  • 3967

Volume


  • 266

Issue


  • 6

Place Of Publication


  • United States