Topological Entropy of Free Product Automorphisms

Details Topological Entropy of Free Product Automorphisms Topological Entropy of Free Product Automorphisms

2000-08-16

arxiv.org/abs/math/0008127v2

Mathematics

Operator Algebras

31 pages, LaTeX, corrected a mistake in the proof of theorem 3.5

Scientific paper

Using free probability constructions involving Cuntz-Pimsner C*-algebras we show that the topological entropy of the free product of two automorphisms is equal to the maximum of the individual entropies. As applications we show that general free shifts have entropy zero. We show that any nuclear C*-dynamical system admits an entropy preserving covariant embedding into the Cuntz algebra on infinitely many generators. It follows that any simple nuclear purely infinite C*-algebra admits an automorphism with any given value of entropy. As a final application we show that if two automorphisms satisfy a CNT-variational principle then so does their free product.

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