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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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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DOI: https://doi.org/10.1007/978-1-4471-6775-4_7
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