Cohomology of graded Lie algebras of Cartan type of characteristic p
type: Item
instance of: scholarly article
title: Cohomology of graded Lie algebras of Cartan type of characteristic p
zbMATH Open document ID: 0636.17005
DOI: 10.1007/BF02941606
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1987-01-01T00:00:00Z
review text: Let F be an algebraically closed field of characteristic \(p>3\) and \(L=\oplus_{i\geq -1}L_{[i]}^ a \)graded Lie algebra of Cartan type over F. For every irreducible \(L_{[0]}\)-module \(V_ 0\) a graded L- module \(\tilde V_ 0\) can be constructed from the tensor product of \(V_ 0\) and the appropriate subalgebra of a divided power algebra. The authors determine the structures of \(H^ 1(L,\tilde V_ 0)\) for \(L=W(2,{\mathfrak m})\), \(W(3,{\mathfrak m})\), or \(H(2,{\mathfrak m})\) and of \(H^ 1_*(L,V)\), where L is any restricted algebra from the above list, and V is an irreducible restricted L-module.
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 4036030
zbMATH Keywords: first cohomology
zbMATH Keywords: cohomology groups
zbMATH Keywords: irreducible restricted module
zbMATH Keywords: graded Lie algebra of Cartan type
zbMATH Keywords: restricted algebra
author: Chiu Sen
author: Guangyu Shen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941606
OpenAlex ID: W4235730782
description: scientific article; zbMATH DE number 4036030