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Analytic Isomorphisms of Transformation Group C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Michael P. Lamoureux
Michael P. Lamoureux*
Affiliation:
Department of Mathematics, Statistics, and Computing Science, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
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Abstract

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An analytic isomorphism of C*-algebras is a C*-isomorphism which maps one distinguished subalgebra, the analytic subalgebra, onto another. A strict partial order of a topological group acting on a topological space determines the analytic subalgebra of the transformation group C*-algebra as a certain non-self-adjoint subalgebra of the C*-algebra. When the group action is free and locally parallel, this analytic subalgebra is locally a subfield of compact operators contained in a reflexive algebra whose subspace lattice is determined by the group order. If in addition the group has the dominated convergence property, an analytic isomorphism of such transformation group C*-algebras induces a homeomorphism of the transformation spaces which maps orbits to orbits. In particular, the C*-algebras for two regular foliations of the plane are analytically isomorphic only if the foliations are topologically conjugate. In the case of parallel actions, a quotient of the group of analytic automorphisms is isomorphic to the second Čech cohomology of a transversal for the action.

Keywords

46L5522D25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 709 - 730
Copyright
Copyright © Canadian Mathematical Society 1990

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