Derivation-simple algebras and the structures of Lie algebras of Witt type
type: Item
instance of: scholarly article
title: Derivation-simple algebras and the structures of Lie algebras of Witt type
zbMATH Open document ID: 0974.17009
author: Yucai Su
author: Xiaoping Xu
author: Zhang Hechun
published in: Journal of Algebra
publication date: 2001-12-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0001178
review text: The authors classify all pairs \((\{ \mathfrak A\}, {\mathfrak D})\) where \(\mathfrak A\) is a commutative associative algebra with identity over an algebraically closed field of characteristic 0, and \(\mathfrak D\) is its finite-dimensional locally finite Abelian derivation subalgebra, such that \(\mathfrak A\) is derivation-simple with respect to \(\mathfrak D\). They also determine the isomorphism classes of the simple Lie algebras of Witt type, which are constructed from such pairs, and explicitly give the structure spaces of these algebras.
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B40
zbMATH DE Number: 1556973
zbMATH Keywords: Abelian derivation subalgebra
zbMATH Keywords: isomorphism classes
zbMATH Keywords: simple Lie algebras of Witt type
MaRDI profile type: Publication
OpenAlex ID: W2070418271
Wikidata QID: Q115395764
arXiv ID: math/0001178
cites work: Generalized Cartan type \(W\) Lie algebras in characteristic zero
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cites work: DESCRIPTION OF FILTERED LIE ALGEBRAS WITH WHICH GRADED LIE ALGEBRAS OF CARTAN TYPE ARE ASSOCIATED
cites work: Lie superalgebras
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cites work: New simple infinite-dimensional Lie algebras of characteristic 0
cites work: Simple Lie algebras of Witt type
cites work: New generalized simple Lie algebras of Cartan type over a field with characteristic 0
cites work: Isomorphisms Between Generalized Cartan Type W Lie Algebras in Characteristic 0
DOI: 10.1006/JABR.2000.8442
description: scientific article