Entropy of automorphisms of II_1-factors arising from the dynamical systems theory

Details Entropy of automorphisms of II_1-factors arising from the dynamical systems theory Entropy of automorphisms of II_1-factors arising from the dynamical systems theory

2000-02-10

arxiv.org/abs/math/0002082v1

Mathematics

Operator Algebras

LaTeX2e, 12 pages

Scientific paper

Let a countable amenable group G acts freely and ergodically on a Lebesgue space (X,mu), preserving the measure mu. If T is an automorphism of the equivalence relation defined by G then T can be extended to an automorphism alpha_T of the II_1-factor M=L^\infty(X,\mu)\rtimes G. We prove that if T commutes with the action of G then H(alpha_T)=h(T), where H(alpha_T) is the Connes- Stormer entropy of alpha_T, and h(T) is the Kolmogorov-Sinai entropy of T. We prove also that for given s and t, 0\le s\le t\le\infty, there exists a T such that h(T)=s and H(alpha_T)=t.

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