Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms
type: Item
instance of: scholarly article
title: Heisenberg Lie superalgebras and their invariant superorthogonal and supersymplectic forms
zbMATH Open document ID: 1264.17007
author: M. C. Rodríguez-Vallarte
author: Gil Salgado
author: O. A. Sánchez-Valenzuela
published in: Journal of Algebra
publication date: 2011-11-08T00:00:00Z
review text: In this paper, the classification problem of finite-dimensional, complex Lie superalgebras of Heisenberg type is considered. It is shown that these superalgebras do not admit invariant supergeometric structures, up to the case of one-dimensional extensions by specific derivations. In this context, sufficiency conditions to guarantee equivalence of extensions are analyzed, leading to a characterization of isometric extensions.
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 5969519
zbMATH Keywords: solvable
zbMATH Keywords: nilpotent Lie (super)algebras
zbMATH Keywords: Heisenberg Lie (super)algebras
zbMATH Keywords: ad-invariant supersymmetric bilinear forms
Wikidata QID: Q115351207
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.02.003
OpenAlex ID: W2059821373
cites work: Q4875318
cites work: Lie superalgebras
cites work: Q3998356
cites work: On Heisenberg-like super group structures
cites work: Solvable Lie algebras with Heisenberg ideals
cites work: The theory of Lie superalgebras. An introduction
DOI: 10.1016/J.JALGEBRA.2011.02.003
Recommended article: Lie superalgebras based on Heisenberg Lie algebras
Recommended article: Representations of Heisenberg Lie super algebras
Recommended article: Darstellungen von Heisenberg-Lie-Superalgebren
Recommended article: Extensions of Lie superalgebras by Heisenberg Lie superalgebras
Recommended article: Heisenberg superalgebras
Recommended article: The Heisenberg-Virasoro Lie conformal superalgebra
Recommended article: Cohomology of Heisenberg Lie superalgebras
Recommended article: Heisenberg superdouble for deformed Poincaré \(k\)-superalgebra and Poincaré-Lie \(k\)-supergroups
Recommended article: Representations of super deformation of Heisenberg-Virasoro type Lie conformal algebras
Recommended article: Q4267899
description: scientific article; zbMATH DE number 5969519