Translative isomorphisms and left-symmetric structures on \(W(m,{\mathbf n})\)
type: Item
instance of: scholarly article
title: Translative isomorphisms and left-symmetric structures on \(W(m,{\mathbf n})\)
zbMATH Open document ID: 0859.17012
published in: Journal of Algebra
publication date: 1996-11-13T00:00:00Z
review text: The author investigates translative isomorphisms of the Cartan-type Lie algebra \(W=W(m,{\mathbf n})\), i.e. isomorphisms of \(W\) into \(W'\dot+{\mathfrak {gl}} (m,{\mathfrak A})\) where \({\mathfrak A}={\mathfrak A}(m,{\mathbf n})\) is the divided power algebra on which \(W\) acts. For some such isomorphisms there is an associated left-symmetric structure on \(W\). The author shows that for a base field of characteristic \(p>0,\) \(W\) admits left-symmetric structures, and furthermore that \(W(m,\mathbf{1})\) admits restricted left-symmetric structures.
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 930158
zbMATH Keywords: translative isomorphisms
zbMATH Keywords: Cartan-type Lie algebra
zbMATH Keywords: left-symmetric structures
author: Guangyu Shen
MaRDI profile type: Publication
full work available at URL: jabr.1996.0276
OpenAlex ID: W2005133222
DOI: 10.1006/JABR.1996.0276
description: scientific article; zbMATH DE number 930158