Entropy for automorphisms of free groups

Author:

Choda Marie

Abstract

Let σ \sigma be the automorphism of the free group F F_\infty which is arising from a permutation of the free generators of F . F_\infty . The σ \sigma naturally induces the automorphism σ ^ \hat \sigma of the reduced C C^* -algebra C r ( F ) , C^*_r(F_\infty ), and also the automorphism σ ^ ¯ \bar {\hat \sigma } of the group factor L ( F ) . L(F_\infty ). We show that the Brown-Germain entropy h a ( σ ) ha(\sigma ) is zero. This implies that the Brown-Voiculescu topological entropy h t ( σ ^ ) , ht(\hat \sigma ), the Connes-Narnhofer-Thirring dynamical entropy h ϕ ( σ ^ ) h_\phi (\hat \sigma ) and the Connes-Størmer entropy H ( σ ^ ¯ ) H(\bar {\hat \sigma } ) are all zero.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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