Crossed products of type I af algebras by abelian groups |
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Authors: | Elliot C Gootman Aldo J Lazar |
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Institution: | (1) School of Mathematical Sciences, Tel Aviv University, 69978 Ramat Aviv, Israel;(2) Present address: Department of Mathematics, University of Georgia, 30602 Athens, GA, USA |
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Abstract: | Let (G, A, α) be a separableC*-dynamical system, withG abelian, and let Γ denote the dual group ofG. We characterize the Γ-invariant ideals of the crossed product algebraG×∩A, and use this characterization to prove that if in additionG is compact andA is type I AF, thenG×∩A is AF also. Finally, assumingG is discrete abelian and bothA andG×∩A are type I. we determine necessary and sufficient conditions, in terms ofA and the isotropy subgroups for the action ofG onÂ, forG×∩A to be AF. |
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