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CONTINUOUS AND DISCRETE FLOWS ON OPERATOR ALGEBRAS

Part of: Connections with other structures, applications Selfadjoint operator algebras

Published online by Cambridge University Press:  01 April 2009

BENJAMÍN A. ITZÁ-ORTIZ
BENJAMÍN A. ITZÁ-ORTIZ*
Affiliation:
Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Carretera Pachuca-Tulancingo Km. 4.5, Pachuca, Hidalgo, 42184, México (email: itza@uaeh.edu.mx)
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Abstract

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Let (N,ℝ,θ) be a centrally ergodic W* dynamical system. When N is not a factor, we show that for each nonzero real number t, the crossed product induced by the time t automorphism θt is not a factor if and only if there exist a rational number r and an eigenvalue s of the restriction of θ to the center of N, such that rst=2π. In the C* setting, minimality seems to be the notion corresponding to central ergodicity. We show that if (A,ℝ,α) is a minimal unital C* dynamical system and A is not simple, then, for each nonzero real number t, the crossed product induced by the time t automorphism αt is not simple if there exist a rational number r and an eigenvalue s of the restriction of α to the center of A, such that rst=2π. The converse is true if, in addition, A is commutative or prime.

Keywords

minimal flowtime t automorphism

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 54H20: Topological dynamics
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 169 - 176
Copyright
Copyright © Australian Mathematical Society 2009

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