In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 86, No. 2 ( 2009-04), p. 169-176
Abstract:
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 θ t 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 =2 π . 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 α t 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 =2 π . The converse is true if, in addition, A is commutative or prime.
Type of Medium:
Online Resource
ISSN:
1446-7887
,
1446-8107
DOI:
10.1017/S1446788708000463
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2009
detail.hit.zdb_id:
1478743-X
SSG:
17,1
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