Maximal solvable subalgebras of Lie superalgebras \({\mathfrak {gl}}(m| n)\) and \({\mathfrak {sl}}(m| n)\)
type: Item
instance of: scholarly article
title: Maximal solvable subalgebras of Lie superalgebras \({\mathfrak {gl}}(m| n)\) and \({\mathfrak {sl}}(m| n)\)
zbMATH Open document ID: 0835.17006
DOI: 10.1007/BF01076514
author: I. M. Shchepochkina
publication date: 1995-09-27T00:00:00Z
review text: For a Lie superalgebra \({\mathfrak g}= {\mathfrak g}_0+ {\mathfrak g}_1= {\mathfrak {sl}} (m|n)\) O. M. Sulim described all its maximal solvable subalgebras \({\mathfrak r}= {\mathfrak r}_0+ {\mathfrak r}_1\), whose even part \({\mathfrak r}_0\) is a Borel subalgebra of the Lie algebra \({\mathfrak g}_0\). In this paper a method for constructing a broader class of maximal solvable subalgebras of the Lie superalgebras \({\mathfrak {gl}} (m|n)\) and \({\mathfrak {sl}} (m|n)\) is presented where the family of Sulim's special superalgebras is obtained as a regular part of the new construction.
Mathematics Subject Classification ID: 17B05
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 795632
zbMATH Keywords: general linear Lie superalgebra
zbMATH Keywords: Lie superalgebras
zbMATH Keywords: maximal solvable subalgebras
reviewed by: Kanat Abdukhalikov
MaRDI profile type: Publication
cites work: Q3733819
cites work: Lie superalgebras
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 795632