The root space decompositions of the quadratic Lie superalgebras
type: Item
instance of: scholarly article
title: The root space decompositions of the quadratic Lie superalgebras
zbMATH Open document ID: 0953.17018
author: Saïd Benayadi
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-05-02T00:00:00Z
full work available at URL: https://eudml.org/doc/228367
full work available at URL: BAG
review text: Let \(\mathfrak g=\mathfrak g_0\oplus \mathfrak g_1\) be a finite dimensional Lie superalgebra over a field of characteristic zero, \(H\) a Cartan subalgebra in \(\mathfrak g_0\). Suppose that there is given a supersymmetric even nondegenerate and \(\mathfrak g\)-invariant form on \(\mathfrak g\). Then \(\mathfrak g\) is basic classical iff the center of \(\mathfrak g\) is trivial and \(\text{ad} _{\mathfrak g}h\) is semisimple for all \(h\in H\). Suppose that the \(\mathfrak g_0\)-module \(\mathfrak g_1\) is semisimple and \(\Delta\) is the set of roots of \(\mathfrak g\) relative to \(H\). Then \(\mathfrak g\) is basic classical iff \(\Delta\) generates the dual space \(H^*\).
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17B05
zbMATH DE Number: 1428673
zbMATH Keywords: Lie superalgebras
reviewed by: Vyacheslav A. Artamonov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1428673