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Entropy for automorphisms of free groups


Author: Marie Choda
Journal: Proc. Amer. Math. Soc. 134 (2006), 2905-2911
MSC (2000): Primary 46L55; Secondary 46L40, 46L89
DOI: https://doi.org/10.1090/S0002-9939-06-08318-3
Published electronically: April 11, 2006
MathSciNet review: 2231614
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Abstract: Let $ \sigma $ be the automorphism of the free group $ F_\infty$ which is arising from a permutation of the free generators of $ F_\infty.$ The $ \sigma $ naturally induces the automorphism $ \hat \sigma $ of the reduced $ C^*$-algebra $ C^*_r(F_\infty),$ and also the automorphism $ \bar{\hat \sigma} $ of the group factor $ L(F_\infty).$ We show that the Brown-Germain entropy $ ha(\sigma )$ is zero. This implies that the Brown-Voiculescu topological entropy $ ht(\hat \sigma ),$ the Connes-Narnhofer-Thirring dynamical entropy $ h_\phi (\hat \sigma )$ and the Connes-Størmer entropy $ H(\bar{\hat \sigma} )$ are all zero.


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Additional Information

Marie Choda
Affiliation: Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara 582-8582, Japan
Email: marie@cc.osaka-kyoiku.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-06-08318-3
Keywords: Entropy, free group, $C^*$-algebra, amenability
Received by editor(s): February 16, 2005
Received by editor(s) in revised form: April 20, 2005
Published electronically: April 11, 2006
Additional Notes: The author was supported in part by JSPS Grant #14540205.
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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