Noncommutative topological entropy of endomorphisms of Cuntz algebras II

TL;DR

This paper extends the study of noncommutative topological entropy in Cuntz algebras to more general endomorphisms, showing that certain entropies equal log N, revealing new entropy invariants.

Contribution

It generalizes previous work by analyzing non-permutation endomorphisms and computes their Voiculescu entropy as log N for specific unitaries.

Findings

Voiculescu entropy of certain endomorphisms equals log N

Extension of entropy analysis beyond permutation-type endomorphisms

Identification of entropy invariants for new classes of endomorphisms

Abstract

A study of noncommutative topological entropy of gauge invariant endomorphisms of Cuntz algebras began in our earlier work with Joachim Zacharias is continued and extended to endomorphisms which are not necessarily of permutation type. In particular it is shown that if H is an N-dimensional Hilbert space, V is an irreducible multiplicative unitary on the tensor product of H with itself and F is the tensor flip, then the Voiculescu entropy of the Longo's canonical endomorphism associated with the unitary VF is equal to log N.