Entropy for automorphisms of free groups

Abstract

Abstract. Let σ be the automorphism of the free group F ∞ which is arising from a permutation of the free generators of F ∞ . The σ naturally induces the automorphismσ of the reduced C * -algebra C * r (F ∞ ), and also the automorphismσ of the group factor L(F ∞ ). We show that the Brown-Germain entropy ha(σ) is zero. This implies that the Brown-Voiculescu topological entropy ht(σ), the Connes-Narnhofer-Thirring dynamical entropy h φ (σ) and the Connes-Størmer entropy H(σ) are all zero.

M$\ddot{o}$bius Disjointness for Exact C$^*$ Algebras

“…This shows that µ is linearly disjoint from (C * r (F Z ), α). By [5], the Voiculescu-Brown entropy ht(α) = 0.…”