Ergodic actions on the fermionic factor. (English) Zbl 0830.46060

Saitô, Kazuyuki; Wright, J. D. Maitland

Q. J. Math., Oxf. II. Ser. 44, No. 176, 493-496 (1993).

From the author’s introduction: Let \(F\) be the Fermion algebra and let \(\widehat {F}\) be its regular \(\sigma\)-completion. Let \(G\) be any countable infinite group

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. In [K. Saito and J. D. M. Wright, Q. J. Math. Oxf., II. Ser. 44, No. 175, 339-343 (1993; Zbl 0821.46078)] we were able to construct a free action

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, \(\beta^G\), of \(G\) on \(\widehat {F}\) (the Bernoulli shift). It is natural to ask when is a Bernoulli shift action on \(\widehat {F}\) ergodic? In this note we show that \(\beta^G\) is an ergodic action on \(\widehat {F}\) for each countable infinite group \(G\).

Reviewer: O.John (Praha)

MSC:

46L60	Applications of selfadjoint operator algebras to physics
46L55	Noncommutative dynamical systems

Keywords:

ergodic action; \(C^*\)-algebra; Fermion algebra

Citations:

Zbl 0821.46078