✦ LIBER ✦

Entropy of Automorphisms of II1-Factors Arising from the Dynamical Systems Theory

✍ Scribed by V.Ya. Golodets; S.V. Neshveyev

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 156 KB
Volume: 181
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3705

No coin nor oath required. For personal study only.

✦ Synopsis

Let a countable amenable group G act freely and ergodically on a Lebesgue space (X, +), preserving the measure +. If T # Aut(X, +) is an automorphism of the equivalence relation defined by G then T can be extended to an automorphism : T of the II 1 -factor M=L (X, +) < G. We prove that if T commutes with the action of G then H(: T )=h(T ), where H(: T ) is the Connes Sto% rmer entropy of : T , and h(T ) is the Kolmogorov Sinai entropy of T. We also prove that for given s and t, 0 s t , there exists a T such that h(T )=s and H(: T )=t.

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