Noncommutative Topological Entropy of Endomorphisms of Cuntz Algebras II

Abstract

A study of noncommutative topological entropy of gauge invariant endomorphisms of Cuntz algebras began in our earlier work with J.\,Zacharias is continued and extended to endomorphisms which are not necessarily of permutation type. In particular it is shown that if $\mathsf{H}$ is an $N$-dimensional Hilbert space, $V$ is an irreducible multiplicative unitary on $\mathsf{H}\otimes \mathsf{H}$ and $F:\mathsf{H}\otimes \mathsf{H}\to \mathsf{H}\otimes \mathsf{H}$ is the tensor flip, then the Voiculescu entropy of the Longo's canonical endomorphism ${\rho }_{VF}\in \text{End}({\mathcal{O}}_N)$ is equal to $\log N$.