1999/04/21 by Neal J. Fowler, Fowler, Neal J. · 3 citations
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA #msc:46L55
paper · pdf · doi:10.48550/arxiv.math/9904115
38 pages, AMS-LaTeX
arxiv created 1999/04/21 · openalex publication_date 1999/04/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = Xs :s∈ P of Hilbert bimodules, indexed by a semigroup P, which are endowed with a multiplication which implements isomorphisms Xs⊗A Xt → Xst; such a family is a called a product system. We define a generalized Cuntz- Pimsner algebra OX, and we show that every twisted crossed product of A by P can be realized as OX for a suitable product system X. Assuming P is quasi- lattice ordered in the sense of Nica, we analyze a certain Toeplitz extension Tcov(X) of OX by embedding it in a crossed product BP ×τ,X P which has been ``twisted'' by X; our main Theorem is a characterization of the faithful representations of BP ×τ,X P.