A note on the Cuntz algebra automorphisms

2024/12/29 by Junyao Pan, Pan, Junyao · 1 citation
Mathematics · #Advanced Topics in Algebra #Advanced Operator Algebra Research #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2412.20318

Abstract

Permutative automorphisms of the Cuntz algebras O_n are in bijection with the stable permutations of [n]^k. They are also the elements of the restricted Weyl group of Aut(O_n). In this note, we characterize a class of stable involutions of [n]². More precisely, we prove Conjecture 12.2 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], and thus providing a new family (with 6 degrees of freedom) of automorphisms of the Cuntz algebras O_n for any n>1.

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• Cuntz algebra automorphisms: transpositions

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