Complexes and vanishing of cohomology for group schemes
type: Item
instance of: scholarly article
title: Complexes and vanishing of cohomology for group schemes
zbMATH Open document ID: 0942.16011
author: Christopher P. Bendel
author: Daniel K. Nakano
published in: Journal of Algebra
publication date: 2000-05-25T00:00:00Z
review text: The notion of completely reducible homology complexes was originally introduced by \textit{D. Benson} and \textit{J. Carlson} [Math. Z. 195, 221-238 (1987; Zbl 0593.20062)] and used to study the question of vanishing of cohomology of finite groups. In this paper the authors study these complexes and the vanishing of cohomology for arbitrary finite-dimensional cocommutative Hopf algebras and for graded, connected, cocommutative Hopf algebras. Applications are given concerning infinitesimal group schemes of reductive and solvable algebraic groups.
Mathematics Subject Classification ID: 16E40
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 14L15
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 1295434
zbMATH Keywords: homology complexes
zbMATH Keywords: cohomology
zbMATH Keywords: cocommutative Hopf algebras
zbMATH Keywords: algebraic groups
zbMATH Keywords: infinitesimal group schemes
reviewed by: Martin D. Crossley
MaRDI profile type: Publication
full work available at URL: jabr.1998.7711
OpenAlex ID: W2014075916
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DOI: 10.1006/JABR.1998.7711
description: scientific article; zbMATH DE number 1295434