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Monotone Complete C*-algebras and Generic Dynamics pp 181–218Cite as

Constructing Monotone Complete C ∗-Algebras

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Abstract

We build monotone complete C ∗-algebras from equivalence relations on topological spaces. This is applied to orbit equivalence relations associated with the action of a countable group G. In general, these algebras may be identified with monotone cross-product algebras arising from actions of G on commutative monotone complete C ∗-algebras. Since different groups can give rise to the same orbit equivalence relation, this can be used to show that, apparently different monotone cross-product algebras, are in fact, isomorphic.

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Author information

Authors and Affiliations

  1. Sendai, Japan

    Kazuyuki Saitô

  2. University of Aberdeen, Aberdeen, Scotland

    J. D. Maitland Wright

  3. Christ Church, University of Oxford, Oxford, UK

    J. D. Maitland Wright

Authors
  1. Kazuyuki Saitô
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  2. J. D. Maitland Wright
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Saitô, K., Wright, J.D.M. (2015). Constructing Monotone Complete C ∗-Algebras. In: Monotone Complete C*-algebras and Generic Dynamics. Springer Monographs in Mathematics. Springer, London. https://doi.org/10.1007/978-1-4471-6775-4_7

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