Cuntz algebra automorphisms: transpositions

2025/07/24 by Junyao Pan, Pan, Junyao
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2507.18358

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

Permutative automorphisms of the Cuntz algebras O_n are in bijection with the stable permutations of [n]^t. They are also the elements of the reduced Weyl group of Aut(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 O_n for any n>1.

Citations

• A note on the Cuntz algebra automorphisms
• All automorphisms of the Calkin algebra are inner

Related

• A note on the Cuntz algebra automorphisms
• Automorphisms of the Cuntz algebras
• Homotopy of inner automorphism groups of Cuntz algebras
• Generalized permutative representations of Cuntz algebras
• The homotopy groups of the automorphism groups of Cuntz-Toeplitz\n algebras