Topological freeness for Hilbert bimodules
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It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description and a simplicity criterion for A ⋊ X ℤ are established.
KeywordsIrreducible Representation American Mathematical Society Faithful Representation Covariant Representation Topological Dynamical System
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- A. B. Antonevich and A. V. Lebedev, Functional Differential Equations: I. C*-theory, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 70, Longman Scientific & Technical, Harlow, 1994.Google Scholar