Lie algebras of CL type
type: Item
instance of: scholarly article
title: Lie algebras of CL type
zbMATH Open document ID: 1072.17009
published in: Journal of Algebra
publication date: 2002-09-08T00:00:00Z
review text: Finite-dimensional simple Lie algebras over an algebraically closed field of characteristic \(p > 7\) are categorized as being of either classical or Cartan type. Additionally, in smaller characteristics there exist simple Lie algebras that do not occur for characteristic \(p > 7\). Yet their structures have close affinities to algebras of either classical or Cartan type. This paper proposes to define these two types in such a way that the finite-dimensional simple Lie algebras of all characteristics can be classified as being of one or the other of these types. The author defines an element \(x\) of a Lie algebra \(L\) to be strongly nilpotent if ad \(x\) is nilpotent and also ad \(y\) is nilpotent for all \(y \in \text{ad}\;x \cdot L\). A simple Lie algebra is said to be of CL type if it has no nonzero strongly nilpotent elements. Otherwise it is said to be of CA type. A number of examples of simple Lie algebras of characteristics 2 and 3 are shown to be of CL type.
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 1797450
zbMATH Keywords: Finite-dimensional simple Lie algebras
zbMATH Keywords: prime characteristic
Wikidata QID: Q115395681
author: Guangyu Shen
MaRDI profile type: Publication
full work available at URL: jabr.2001.9059
OpenAlex ID: W2102788711
cites work: A Class of Simple Lie Algebras of Characteristic Three
cites work: On the structure of some Lie algebras of Kuznetsov
cites work: Families of simple lie algebras of characteristic two
cites work: About two classes of simple Lie algebras over a field of characteristic 3
cites work: Universal graded Lie algebras
cites work: Die adjungierten Darstellungen der Chevalley-Gruppen
cites work: Q4750828
cites work: ad-nilpotent elements, quasi-nilpotent elements and invariant filtrations of infinite dimensional Lie algebras of Cartan type
cites work: DESCRIPTION OF FILTERED LIE ALGEBRAS WITH WHICH GRADED LIE ALGEBRAS OF CARTAN TYPE ARE ASSOCIATED
cites work: Q3824547
cites work: Q4735307
cites work: Non-alternating hamiltonian algebraP(n,m)of characteristic two
cites work: Q3866253
cites work: Q3726306
cites work: Q3129416
cites work: NEW SERIES OF SIMPLE LIE ALGEBRAS OF CHARACTERISTIC 3
cites work: A contragredient Lie algebra of dimension 29 over a field of characteristic 3
cites work: Q4039778
cites work: Classification of simple Lie algebras over algebraically closed fields of prime characteristic
cites work: Q5656907
cites work: A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic
cites work: Lie algebra \(K(n,{{\mu{}}_ j},m)\) of Cartan type of characteristic \(p=2\)
DOI: 10.1006/JABR.2001.9059
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description: scientific article; zbMATH DE number 1797450