Positive Voiculescu-Brown entropy in noncommutative toral automorphisms

Details Positive Voiculescu-Brown entropy in noncommutative toral automorphisms Positive Voiculescu-Brown entropy in noncommutative toral automorphisms

2003-03-07

arxiv.org/abs/math/0303090v1

Mathematics

Operator Algebras

13 pages

Scientific paper

We show that the Voiculescu-Brown entropy of a noncommutative toral automorphism arising from a matrix S in GL(d,Z) is at least half the value of the topological entropy of the corresponding classical toral automorphism. We also obtain some information concerning the positivity of local Voiculescu-Brown entropy with respect to single unitaries. In particular we show that if S has no roots of unity as eigenvalues then the local Voiculescu-Brown entropy with respect to every product of canonical unitaries is positive, and also that in the presence of completely positive CNT entropy the unital version of local Voiculescu-Brown entropy with respect to every non-scalar unitary is positive.

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