Stable outer conjugacy and strong Morita equivalence of group actions on pro-C
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Authors: | Maria Joi?a |
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Institution: | (1) Department of Mathematics, University of Bucharest, Bucharest, Romania |
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Abstract: | We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C
*-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E
*(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E
*) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes Proc. London
Math. Soc. 49(1984), 289–306].
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Keywords: | Group actions Strong Morita equivalence Pro-C *-algebras Hilbert modules |
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