Lie algebras with maximality condition for Abelian subalgebras.
type: Item
instance of: scholarly article
title: Lie algebras with maximality condition for Abelian subalgebras.
zbMATH Open document ID: 1106.17304
author: S. A. Pikhtil'kov
author: K. I. Beidar
author: Mikhail Zaicev
published in: Moscow University Mathematics Bulletin
publication date: 2004-03-21T00:00:00Z
review text: The authors study special Lie algebras over an arbitrary field. It is shown that the maximality condition for the Abelian subalgebras yields finite dimensionality for any generally special algebra. As a corollary an equivalence of two conditions of finite dimensionality of the algebra and Noetherianness of its universal enveloping algebra is established for the given class of Lie algebras.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 2061512
zbMATH Keywords: Lie algebras
zbMATH Keywords: minimal condition
zbMATH Keywords: maximal condition
zbMATH Keywords: finite-dimensionality
zbMATH Keywords: Noetherian universal enveloping algebras
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2061512