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Positive Voiculescu-Brown entropy in noncommutative toral automorphisms by Kerr, David; Li, Hanfeng is a scholarly article available to read on EtoBox.

What is Positive Voiculescu-Brown entropy in noncommutative toral automorphisms about?

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.

Author

Kerr, David; Li, Hanfeng

Published

2003

Language

EN