1-cohomology of Chevalley groups
type: Item
instance of: scholarly article
title: 1-cohomology of Chevalley groups
zbMATH Open document ID: 0687.20039
DOI: 10.1016/0021-8693(89)90257-3
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let G be a Chevalley group over the finite field \({\mathbb{F}}_ q\) and let B denote a Borel subgroup. The author considers extensions between the trivial module and simple modules. If the highest weight \(\lambda\) of the simple module is a fundamental weight he proves that except for a few cases where \(q\leq 3\) any such extension is realized as a quotient of the G-module induced from the B-module \(\lambda\). He also establishes the same result for general \(\lambda\) in many cases - including all cases where q is not a prime.
reviewed by: Henning Haahr Andersen
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 4125690
zbMATH Keywords: Chevalley group
zbMATH Keywords: Borel subgroup
zbMATH Keywords: extensions
zbMATH Keywords: simple modules
zbMATH Keywords: highest weight
author: Helmut Völklein
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90257-3
OpenAlex ID: W2013034711
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description: scientific article; zbMATH DE number 4125690