Dynamical systems and commutants in crossed products
Silvestrov, Sergei; Svensson, Christian; de Jeu, Marcel (2007). Dynamical systems and commutants in crossed products. International Journal of Mathematics, 18, (4), 455 - 471
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Published
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English
Authors:
Silvestrov, Sergei
;
Svensson, Christian
;
de Jeu, Marcel
Department:
Mathematics (Faculty of Engineering)
Non-commutative Geometry-lup-obsolete
Project:
Non-commutative Analysis of Dynamics, Fractals and Wavelets
Research Group:
Non-commutative Geometry-lup-obsolete
Abstract:
In this paper, we describe the commutant of an arbitrary subalgebra A of the algebra of functions on a set X in a crossed product of A with the integers, where the latter act on A by a composition automorphism defined via a bijection of X. The resulting conditions which are necessary and sufficient for A to be maximal abelian in the crossed product are subsequently applied to situations where these conditions can be shown to be equivalent to a condition in topological dynamics. As a further step, using the Gelfand transform, we obtain for a commutative completely regular semi-simple Banach algebra a topological dynamical condition on its character space which is equivalent to the algebra being maximal abelian in a crossed product with the integers.
Keywords:
maximal abelian subalgebra ;
Crossed product ;
completely regular Banach algebra ;
dynamical system
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