Partial-isometric crossed products by semigroups of endomorphisms

2002/10/23 by Janny Lindiarni, Lindiarni, Janny, Iain Raeburn +1 · 3 citations
Mathematics · #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L05

paper · pdf · doi:10.48550/arxiv.math/0210364

26 pages

arxiv created 2002/10/23 · openalex publication_date 2002/10/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ⁺ be the positive cone in a totally ordered abelian group Γ, and let α be an action of Γ⁺ by endomorphisms of a C^*-algebra A. We consider a new kind of crossed-product C^*-algebra A×_αΓ⁺, which is generated by a faithful copy of A and a representation of Γ⁺ as partial isometries. We claim that these crossed products provide a rich and tractable family of Toeplitz algebras for product systems of Hilbert bimodules, as recently studied by Fowler, and we illustrate this by proving detailed structure theorems for actions by forward and backward shifts.

Cited by

• Stacey crossed products associated to Exel systems
• The Nica-Toeplitz algebras of dynamical systems over abelian lattice-ordered groups as full corners
• Iterating the Pimsner construction

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