Permutative automorphisms of the Cuntz algebras: quadratic cycles, an involution and a box product
type: Item
instance of: scholarly article
title: Permutative automorphisms of the Cuntz algebras: quadratic cycles, an involution and a box product
author: Francesco Brenti
author: Roberto Conti
author: Gleb V. Nenashev
published in: Advances in Applied Mathematics
publication date: 2022-12-08T00:00:00Z
review text: This work can be read as a continuation of \textit{F. Brenti} and \textit{R. Conti} [Adv. Math. 381, Article ID 107590, 61 p. (2021; Zbl 1459.05347)] where the study of stable permutations on \(n^r\) elements is undertaken. These stable permutations are graded by the notion of rank. The ultimate goal is to gain an understanding of the Weyl groups of the Cuntz algebras. The more immediate desire is to characterize and enumerate the stable permutations of a given rank. In this work, the authors achieve this for transpositions of rank one, for 3-cycles of rank at most 2, and for a restricted class of 4-cycles. On this basis, they conjecture that a stable \(r\)-cycle has rank at most \(r - 1\). They also introduce two rank-preserving algebraic operations on the set of stable permutations: (i) an involution that preserves cycle structure and (ii) a binary operation that associates to permutations on \(n^r\) and \(m^r\) objects, respectively, a permutation on \((nm)^r\) objects.
Mathematics Subject Classification ID: 05E16
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 46L40
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 7628621
zbMATH Keywords: permutation
zbMATH Keywords: stability
zbMATH Keywords: rank
zbMATH Keywords: enumeration
reviewed by: Alberto Luis Delgado
MaRDI profile type: Publication
full work available at URL: j.aam.2022.102447
OpenAlex ID: W4307729085
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DOI: 10.1016/J.AAM.2022.102447
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description: scientific article; zbMATH DE number 7628621