The partial-isometric crossed products by semigroups of endomorphisms are Morita equivalent to crossed products by groups

2017/10/18 by Zahmatkesh, Saeid
#46L55 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1710.06708

Abstract

Let Γ⁺ be the positive cone of a totally ordered abelian discrete group Γ, and α an action of Γ⁺ by extendible endomorphisms of a C^*-algebra A. We prove that the partial-isometric crossed product A×_α^\textrmpisoΓ⁺ is a full corner of a group crossed product B×_βΓ, where B is a subalgebra of ℓ^∞(Γ,A) generated by a collection of faithful copies of A, and the action β on B is induced by shift on ℓ^∞(Γ,A). We then use this realization to show that A×_α^\textrmpisoΓ⁺ has an essential ideal J, which is a full corner in an ideal I×_βΓ of B×_βΓ.

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