On semisimple Lie algebras over algebraically closed fields
type: Item
instance of: scholarly article
title: On semisimple Lie algebras over algebraically closed fields
zbMATH Open document ID: 0583.17006
author: Takeshi Hirai
published in: Proceedings of the Japan Academy. Series A
publication date: 1984-01-01T00:00:00Z
review text: The author studies so-called standard representatives, and their adjoint actions, of nilpotent classes of a Lie algebra over an algebraically closed field obtained from a Chevalley basis of a complex semisimple Lie algebra; they are a special kind of sums of distinct root vectors from a Chevalley basis. Various results depending on the characteristic and the type are stated; there are no proofs.
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 3933281
zbMATH Keywords: standard representatives
zbMATH Keywords: nilpotent classes
zbMATH Keywords: complex semisimple Lie algebra
zbMATH Keywords: root vectors
zbMATH Keywords: Chevalley basis
reviewed by: H. de Vries
MaRDI profile type: Publication
full work available at URL: pjaa.60.225
OpenAlex ID: W2006875369
cites work: Semisimple subalgebras of semisimple Lie algebras
cites work: On Richardson classes of unipotent elements in semisimple algebraic groups
cites work: Completely Reducible Lie Algebras of Linear Transformations
cites work: Nilpotent classes and sheets of Lie algebras in bad characteristic
cites work: Q5662587
DOI: 10.3792/PJAA.60.225
description: scientific article; zbMATH DE number 3933281