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Crossed Product C*-Algebras Associated wth Homeomorphisms of the Unit Circle


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1 347 Sorauren Ave., suite 222, Toronto, Ontario, M6R 2G5, Canada
     

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Given a homeomorphism ϕ of the unit circle T, there is associated the C*-crossed product algebra of C(T) by the Z-action induced by ϕ. We analyze the C*-crossed product algebras arising from those homeomorphisms that possess both cyclic and non-cyclic points, or are order-reversing. It is shown that upto compact perturbations, infinite-dimensional irreducible *-representations of algebras in this class can be expressed in terms of certain finite-dimensional irreducible *-representations. This relationship is used to recover the topological features of the underlying homeomorphisms upto inversion, and to construct a complete *-isomorphism invariant for these algebras. It is shown that two algebras with underlying homeomorphisms ϕ and ψ are *-isomorphic if and only if ϕ is conjugate to ψ or ψ −1.
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  • Crossed Product C*-Algebras Associated wth Homeomorphisms of the Unit Circle

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Authors

Alessandro De Rango
347 Sorauren Ave., suite 222, Toronto, Ontario, M6R 2G5, Canada

Abstract


Given a homeomorphism ϕ of the unit circle T, there is associated the C*-crossed product algebra of C(T) by the Z-action induced by ϕ. We analyze the C*-crossed product algebras arising from those homeomorphisms that possess both cyclic and non-cyclic points, or are order-reversing. It is shown that upto compact perturbations, infinite-dimensional irreducible *-representations of algebras in this class can be expressed in terms of certain finite-dimensional irreducible *-representations. This relationship is used to recover the topological features of the underlying homeomorphisms upto inversion, and to construct a complete *-isomorphism invariant for these algebras. It is shown that two algebras with underlying homeomorphisms ϕ and ψ are *-isomorphic if and only if ϕ is conjugate to ψ or ψ −1.