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Journal of Operator Theory

Volume 37, Issue 1, Winter 1997  pp. 67-89.

Induced representations of twisted C*-dynamical systems

Authors: S. Kaliszewski
Author institution:Department of Mathematics, University of Newcastle, NSW 2308, AUSTRALIA

Summary: Let $(A, G, \alpha, u)$ be a twisted C*-dynamical system in the sense of Busby and Smith. Then for any closed subgroup H of G, $A \times _{\alpha ,u} H$ is Morita equivalent to $C_0 (G/H,A) \times _{\tilde \alpha ,\tilde u} G$, where $(\tilde a,\tilde u)$ is the diagonal twisted action. We show that the space of compactly supported bounded Borel functions B_c(G, A) can be given a natural pre-imprimitivity bimodule structure which implements the equivalence, and use this to induce representations from $A \times _{\alpha ,u} H$ to $A \times _{\alpha ,u} G$. We prove an imprimitivity theorem for this inducing process, and show how the inducing processes of Busby and Smith and Mackey are special cases of ours.

Keywords: C*-algebra, dynamical system, Morita equivalence.

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