The C^*-envelope of a semicrossed product and Nest Representations

2008/10/29 by Justin R. Peters, Peters, Justin R.
Mathematics · #37B99 #46L52 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #math.DS #math.OA #msc:37B99 #msc:46L52

paper · pdf · doi:10.48550/arxiv.0810.5364

arxiv created 2008/10/29 · arxiv updated 2009/12/01

Abstract

Let X be compact Hausdorff, and ϕ: X → X a continuous surjection. Let A be the semicrossed product algebra corresponding to the relation fU = Uf∘ ϕ or to the relation Uf = f∘ ϕU. Then the C^*-envelope of A is the crossed product of a commutative C^*-algebra which contains C(X) as a subalgebra, with respect to a homeomorphism which we construct. We also show there are"sufficiently many" nest representations.

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