Cuntz algebra automorphisms: transpositions

TL;DR

This paper characterizes the stability of transpositions in the symmetric group acting on triples, leading to a new family of automorphisms of Cuntz algebras with six degrees of freedom for any n>1.

Contribution

It provides a characterization of transposition stability in $S([n]^3)$, introducing a new family of automorphisms of Cuntz algebras with six degrees of freedom.

Findings

Characterization of stable transpositions in $S([n]^3)$

Introduction of a new family of automorphisms with six degrees of freedom

Applicable to all $n > 1$

Abstract

Permutative automorphisms of the Cuntz algebras $\mathcal{O}_n$ are in bijection with the stable permutations of $[n]^t$. They are also the elements of the reduced Weyl group of $Aut(\mathcal{O}_n)$. In this paper, we characterize the stability of transpositions in $S([n]^3)$, and thus providing a new family (with $6$ degrees of freedom) of automorphisms of the Cuntz algebras $\mathcal{O}_n$ for any $n>1$.