A further generalization of algebras of Cartan type \(W\)
type: Item
instance of: scholarly article
title: A further generalization of algebras of Cartan type \(W\)
zbMATH Open document ID: 0955.17015
author: Yanyan Li
published in: Journal of Algebra
publication date: 2001-03-04T00:00:00Z
review text: Over a field \(F\) of characteristic 0, the author extends the (infinite-dimensional) Lie algebra of Cartan type \(W\), which is by definition the derivation algebra of the polynomial algebra (of \(n\) indeterminates), to the Lie algebra \(\widetilde{W}^*:= \operatorname {Der} F(x_1,\dots, x_n)\), the derivation algebra of the algebra of rational functions. The author shows that \(\widetilde{W}^*\) is simple. When \(n=1\), it is proved that every derivation of \(\widetilde{W}^*\) is inner.
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B40
zbMATH DE Number: 1423884
zbMATH Keywords: Lie algebra of Cartan type \(W\)
zbMATH Keywords: derivation algebra
zbMATH Keywords: algebra of rational functions
reviewed by: Guangyu Shen
MaRDI profile type: Publication
full work available at URL: jabr.1999.8065
OpenAlex ID: W2000757735
cites work: New simple infinite-dimensional Lie algebras of characteristic 0
cites work: Q4217859
cites work: Generalizations of Witt algebras over a field of characteristic zero
DOI: 10.1006/JABR.1999.8065
description: scientific article; zbMATH DE number 1423884