Some remarks on solvable Lie superalgebras
type: Item
instance of: scholarly article
title: Some remarks on solvable Lie superalgebras
zbMATH Open document ID: 0839.17005
DOI: 10.1016/0022-4049(94)E0132-2
author: Kristien Bauwens
author: Lieven Le Bruyn
published in: Journal of Pure and Applied Algebra
publication date: 1995-07-03T00:00:00Z
review text: The authors investigate the classification problem for (solvable) Lie superalgebras. In particular, they settle the case when the even part is a solvable Lie algebra \(\mathfrak g\) and the odd part is a two-dimensional representation of \(\mathfrak g\). They also point out which of these solvable superalgebras fail to be completely solvable; this is the exception, not the rule. One technique used is to see how, once one fixes some Lie algebra \(\mathfrak g\), the superalgebra changes as one varies the odd part in the space of representations of \(\mathfrak g\) (of a fixed dimension). Especially, the authors determine the possibilities when the representation is semisimple. In addition, it is shown that if the bilinear form on the odd part of a Lie superalgebra is non-degenerate then the microlocalisation of the enveloping algebra at the symmetrisation of determinant of the matrix of the bilinear form is a maximal order of finite global dimension.
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 762331
zbMATH Keywords: solvable Lie superalgebras
zbMATH Keywords: classification
zbMATH Keywords: microlocalisation
zbMATH Keywords: enveloping algebra
Wikidata QID: Q115364394
reviewed by: Martin P. Holland
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 762331