A note on the Cuntz algebra automorphisms
Junyao Pan

TL;DR
This paper characterizes a specific class of involutions in the automorphisms of Cuntz algebras, confirming a conjecture and expanding the known family of automorphisms with new degrees of freedom.
Contribution
It proves a conjecture about stable involutions, introducing a new family of automorphisms of Cuntz algebras with six degrees of freedom.
Findings
Confirmed Conjecture 12.2 of Brenti and Conti
Identified a new family of automorphisms with 6 degrees of freedom
Characterized stable involutions of [n]^2
Abstract
Permutative automorphisms of the Cuntz algebras are in bijection with the stable permutations of . They are also the elements of the restricted Weyl group of . In this note, we characterize a class of stable involutions of . More precisely, we prove Conjecture 12.2 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], and thus providing a new family (with degrees of freedom) of automorphisms of the Cuntz algebras for any .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Operator Algebra Research · Holomorphic and Operator Theory
