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Morita-Rieffel equivalence and spectral theory for integrable automorphism groups of C*-algebras

机译:C *-代数可积自同构群的Morita-Rieffel等价和谱理论

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Given a C*-dynamical system (A, G,a), we discuss conditions under which subalgebras of the multiplier algebra M(A) consisting of fixed points for alpha are Morita-Rieffel equivalent to ideals in the crossed product of A by G. In case G is abelian we also develop a spectral theory, giving a necessary and sufficient condition for alpha to be equivalent to the dual action on the cross-sectional C*-algebra of a Fell bundle. In our main application we show that a proper action of an abelian group on a locally compact space is equivalent to a dual action. (C) 2000 Academic Press. [References: 21]
机译:给定一个C *动力系统(A,G,a),我们讨论由α的固定点组成的乘数代数M(A)的子代数的Morita-Rieffel等于A与G的乘积的理想条件的条件。在G是阿贝尔的情况下,我们还发展了一个谱理论,给出了一个必要和充分的条件,使得α等于对Fell束的截面C *-代数的双重作用。在我们的主要应用中,我们证明了阿贝尔群在局部紧空间上的适当作用等同于双重作用。 (C)2000学术出版社。 [参考:21]

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