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Semigroup C∗-Algebras

  • Conference paper
Operator Algebras and Applications

Part of the book series: Abel Symposia ((ABEL,volume 12))

Abstract

This is a survey article about recent developments in semigroup C*-algebras. These C*-algebras generated by left regular representations of semigroups have been studied for some time, but it was only recently that several new connections and results were discovered, triggered by particularly interesting examples from number theory and group theory. We explain the construction of semigroup C*-algebras, introduce the basic underlying algebraic objects, define two important conditions called Toeplitz condition and independence, and present results concerning amenability and nuclearity, K-theory, and classification.

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Acknowledgements

Research supported by EPSRC grant EP/M009718/1.

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Authors and Affiliations

  1. School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

    Xin Li

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  1. Xin Li
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Correspondence to Xin Li .

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Editors and Affiliations

  1. Department of Science and Technology, University of the Faroe Islands, Tórshavn, Faroe Islands

    Toke M. Carlsen

  2. Department of Mathematics, University of Oslo, Oslo, Norway

    Nadia S. Larsen

  3. Department of Mathematics, University of Oslo, Oslo, Norway

    Sergey Neshveyev

  4. Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway

    Christian Skau

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Li, X. (2016). Semigroup C∗-Algebras. In: Carlsen, T.M., Larsen, N.S., Neshveyev, S., Skau, C. (eds) Operator Algebras and Applications. Abel Symposia, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-39286-8_9

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