Vector and covector invariants of Lie superalgebras
type: Item
instance of: scholarly article
title: Vector and covector invariants of Lie superalgebras
zbMATH Open document ID: 0876.17030
DOI: 10.1007/BF02509513
publication date: 1997-06-25T00:00:00Z
review text: In the paper under review the author continues his research from his previous paper [\textit{A. N. Sergeev}, Funkts. Anal. Prilozh. 26, No. 3, 88-90 (1992; Zbl 0838.17036)]. Let \(\mathfrak g\) be a subsuperalgebra of the Lie superalgebra \({\mathfrak gl}(V)\) of a finite dimensional superspace \(V\) over \(\mathbb{C}\). By invariant theory of \(\mathfrak g\) the author means the study of \(\mathfrak g\)-invariants in \({\mathfrak A}_{k,l}^{p,q}=S(V^k\oplus\pi(V)^l\oplus V^{\ast p}\oplus \pi(V^{\ast})^q)\). This symmetric algebra is isomorphic to \(S(U\otimes V\oplus V^{\ast}\otimes W)\), where \(U\) and \(W\) are superspaces of dimensions \((k,l)\) and \((p,q)\), respectively. In his previous paper the author described the generators of the algebra of \(\mathfrak g\)-invariants for each series of classical superalgebras and their central extensions. The generators were given up to the action of polarization operators, i.e. up to multiplication with elements of universal enveloping algebras. Now, the author generalizes these results and announces sets of generators (in the usual sense, not taking into account the action of the polarization operators) for the superalgebras \(\text{sl}(V)\), \(\text{osp}(V)\) and \(\text{sp}(V)\).
Mathematics Subject Classification ID: 17B70
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 22E99
zbMATH DE Number: 1023831
zbMATH Keywords: invariant theory of Lie superalgebras
zbMATH Keywords: classical Lie superalgebras
zbMATH Keywords: generators
author: Alexander Sergeev
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
cites work: Q5772226
cites work: Q3947818
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1023831