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.
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This work was in part supported by Polish National Science Centre grant number DEC-2011/01/D/ST1/04112.
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Kwaśniewski, B.K. Topological freeness for Hilbert bimodules. Isr. J. Math. 199, 641–650 (2014). https://doi.org/10.1007/s11856-013-0057-0