\(R\)-matrices for Leibniz algebras
type: Item
instance of: scholarly article
title: \(R\)-matrices for Leibniz algebras
zbMATH Open document ID: 1053.17003
DOI: 10.1023/A:1023067727095
author: Raúl Felipe
author: F. Ongay
author: Nancy López Reyes
published in: Letters in Mathematical Physics
publication date: 2003-07-01T00:00:00Z
review text: The authors introduce \(R\)-matrices for Leibniz algebras as a direct generalization of the classical \(R\)-matrices. The linear mapping \(R_{\pm}: L\to L\) of a Leibniz algebra \(L\) is called an \(R_{\pm}\)-matrix if the new bilinear operator defined by \([X,Y]_{R_{\pm}}=[RX,Y]\pm [X,RY]\), \(X,Y\in L\), satisfies the Jacobi-Leibniz identity. The authors prove that \(R\) is an \(R_{\pm}\)-matrix if it satisfies a Yang-Baxter type equation. In the concluding remarks they outline possible relations of their constructions to integrable systems.
Mathematics Subject Classification ID: 17A32
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 17B80
zbMATH DE Number: 1944890
zbMATH Keywords: Leibniz algebras
zbMATH Keywords: R-matrices
zbMATH Keywords: Yang-Baxter equations
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
full work available at URL: a:1023067727095
OpenAlex ID: W1574830344
description: scientific article; zbMATH DE number 1944890