Criterion for \(\text{SL}(2,\mathbb{Z})\)-matrix to be conjugate to its inverse
type: Item
instance of: scholarly article
title: Criterion for \(\text{SL}(2,\mathbb{Z})\)-matrix to be conjugate to its inverse
zbMATH Open document ID: 1022.20021
DOI: 10.1142/S0252959902000419
published in: Chinese Annals of Mathematics. Series B
publication date: 2003-04-14T00:00:00Z
review text: Recently, L. Polterovich and Z. Rudnick in a preprint proved that an element \(h\in\text{SL}(2,\mathbb{Z})\) is stably mixing if and only if it is not conjugate to its inverse in \(\text{SL}(2,\mathbb{Z})\). The author of this paper gives a necessary and sufficient condition for a matrix in \(\text{SL}(2,\mathbb{Z})\) to be conjugate to its inverse. This condition reduces the determination of conjugation to solving an indeterminate equation of second degree.
Mathematics Subject Classification ID: 20H05
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 20E45
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 1877198
zbMATH Keywords: 2-dimensional special linear group over the integers
zbMATH Keywords: conjugation
zbMATH Keywords: inverses
zbMATH Keywords: mixed stability
author: Yiming Long
MaRDI profile type: Publication
full work available at URL: s0252959902000419
OpenAlex ID: W2159162622
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description: scientific article; zbMATH DE number 1877198