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Positive Voiculescu–Brown entropy in non-commutative toral automorphisms

2006; Cambridge University Press; Volume: 26; Issue: 06 Linguagem: Inglês

10.1017/s0143385706000563

1469-4417

David Kerr, Hanfeng Li,

Algebraic structures and combinatorial models

We show that the Voiculescu–Brown entropy of a non-commutative toral automorphism arising from a matrix 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.