Lie structures on differential algebras
type: Item
instance of: scholarly article
title: Lie structures on differential algebras
zbMATH Open document ID: 0683.17015
author: Fujio Kubo
author: Fumitake Mimura
published in: Hiroshima Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let L be an n-dimensional Lie algebra over a field t of characteristic zero, \(A\supseteq L\) a commutative associative algebra over t with an identity. In this paper, the author extends the Lie structure from L to A by means of derivations \(d_ 1,...,d_ n\) of A satisfying \(d_ id_ j=d_ jd_ i\), \(d_ i(x_ j)=\delta_{ij}\) \((x_ i\) is a basis of L): \([a,b]=\sum [x_ i,x_ j]d_ i(a)d_ j(b)\). After showing a way to give a Lie structure on a localization of A (A is assumed to be an integral domain), the author studies the Lie structures on the formal power series \(t[x_ 1,...,x_ n]\) and on factor algebras of polynomial algebras \(t[x_ 1,...,x_ n,y]/(y^ 2-2y+\beta).\)
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 16U10
Mathematics Subject Classification ID: 13N05
Mathematics Subject Classification ID: 12H05
zbMATH DE Number: 4118551
zbMATH Keywords: differential algebra
zbMATH Keywords: derivations
zbMATH Keywords: integral domain
zbMATH Keywords: Lie structures
zbMATH Keywords: formal power series
zbMATH Keywords: factor algebras of polynomial algebras
reviewed by: Jan Kubarski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1206129613
OpenAlex ID: W1511561871
DOI: 10.32917/HMJ/1206129613
description: scientific article; zbMATH DE number 4118551