Itzá-Ortiz, B., Continuous and discrete flows on operator algebras, Journal of the Australian Mathematical Society 86 (2009), 169--176. Preprinted
Let (N, R, ) be a centrally ergodic W* dynamical system. When N is not a factor, we show that, for each t 6= 0, the crossed product induced by the time t automorphism t is not a factor if and only if there exist a rational number r and an eigenvalue s of the restriction of to the center of N, such that rst = 2. In the C* setting, minimality seems to be the notion corresponding to central ergodicity. We show that if (A, R, ) is a minimal unital C* dynamical system and A is either prime or commutative but not simple, then, for each t 6= 0, the crossed product induced by the time t automorphism t is not simple if and only if there exist a rational number r and an eigenvalue s of the restriction of to the center of A, such that rst = 2.
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