Socle and some invariants of quadratic Lie superalgebras
type: Item
instance of: scholarly article
title: Socle and some invariants of quadratic Lie superalgebras
zbMATH Open document ID: 1013.17029
DOI: 10.1016/S0021-8693(02)00682-8
author: Saïd Benayadi
published in: Journal of Algebra
publication date: 2003-05-04T00:00:00Z
review text: Let \(\mathfrak g\) be a Lie superalgebra with a nondegenerate bilinear function \(B(x,y)\) such that \(B(x,y)=(-1)^{ab}B(y,x)\) if \(x\in {\mathfrak g}_a, y\in {\mathfrak g}_b\); \(B([x,y],z)=B(x,[y,z])\) for all \(x,y,z\in \mathfrak g\); \(B(x,y)=0\) if \(x\in {\mathfrak g}_0, y\in {\mathfrak g}_1\). In the first sections of the paper minimal graded ideals and the socle of \(\mathfrak g\) are considered. These results are applied to a characterization of simple Lie superalgebras. In the third section a problem of uniqueness of the function \(B\) is considered. In the final section some properties of new invariants related to the socle are discussed and a converse of Koszul's theorem is established.
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 1903595
zbMATH Keywords: simple Lie superalgebras
zbMATH Keywords: minimal graded ideals
zbMATH Keywords: socle
zbMATH Keywords: invariants
zbMATH Keywords: converse of Koszul's theorem
reviewed by: Vyacheslav A. Artamonov
Wikidata QID: Q115340510
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1903595