New parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and some explicit formulas for its logarithm
type: Item
instance of: scholarly article
title: New parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and some explicit formulas for its logarithm
zbMATH Open document ID: 1489.22014
published in: Journal of Geometry and Symmetry in Physics
publication date: 2021-09-08T00:00:00Z
review text: The exponential map for Lie groups has been extensively studied and it is neither injective nor surjective in general, as it is already the case for \(\mathrm{SL}(2,\mathbb R)\), the Lie group of invertible \(2\times 2\) real matrices. In the paper under review, the authors give a new parametrization of \(\mathrm{SL}(2,\mathbb R)\) and derive explicit formulas for the inverse of the exponential map. Moreover a geometric description of the field of values of matrices in \(\mathrm{SL}(2,\mathbb R)\) is given in terms of ellipses.
reviewed by: Salah Mehdi
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 17B81
Mathematics Subject Classification ID: 81R05
zbMATH DE Number: 7392462
zbMATH Keywords: parameterization of \(\mathrm{SL}(2,\mathbb{R})\)-matrices
zbMATH Keywords: logarithm of \(\mathrm{SL}(2,\mathbb{R})\)-matrices
zbMATH Keywords: field of values
author: Tihomir I. Valchev
author: Clementina Mladenova
author: Ivaïlo Mladenov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7392462