Deformations of the Lie algebra of type \(G_2\) of characteristic 3
type: Item
instance of: scholarly article
title: Deformations of the Lie algebra of type \(G_2\) of characteristic 3
zbMATH Open document ID: 1009.17016
author: S. A. Kirillov
author: N. G. Chebochko
author: Michael Kuznetsov
published in: Russian Mathematics
publication date: 2000-12-07T00:00:00Z
review text: The authors prove that the exceptional classical Lie algebra \(L\) of type \(G_2\) over an algebraically closed field of characteristic \(p=3\) is rigid, i.e. with respect to the Zariski topology on the variety of the Lie algebra structures on the vector space of \(L\) there exists a neighborhood of \(L\) all of whose points are Lie algebras isomorphic to \(L\). This is accomplished by proving that the cohomology group \(H^2(L,L)=0\).
Mathematics Subject Classification ID: 17B56
Mathematics Subject Classification ID: 17B50
zbMATH DE Number: 1541592
zbMATH Keywords: rigidity
zbMATH Keywords: characteristic three
zbMATH Keywords: vanishing cohomology group
zbMATH Keywords: type \(G_2\)
zbMATH Keywords: exceptional classical Lie algebra
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1541592