On the geometry of the adjoint representation of a Chevalley group
type: Item
instance of: scholarly article
title: On the geometry of the adjoint representation of a Chevalley group
zbMATH Open document ID: 0688.20022
DOI: 10.1016/0021-8693(89)90279-2
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let L be the Lie algebra of a linear algebraic group G over a field of arbitrary characteristic. The subalgebras of L corresponding to long root subgroups are called long root subalgebras of L. Subalgebras of L generated by long root subalgebras are called long subalgebras. The main theorem: Let L correspond to a simple group G of type different from \(C_ n\) and \(A_ 1\). Then L has a presentation with generators the elements of its long root subalgebras, subject to those relations that hold inside long \(A_ 2\)-subalgebras.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 4127499
zbMATH Keywords: Lie algebra of a linear algebraic group
zbMATH Keywords: long root subgroups
zbMATH Keywords: long root subalgebras
zbMATH Keywords: presentation
author: Helmut Völklein
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90279-2
OpenAlex ID: W2074812633
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description: scientific article; zbMATH DE number 4127499