Irreducible non-Lie modules for Malcev superalgebras
type: Item
instance of: scholarly article
title: Irreducible non-Lie modules for Malcev superalgebras
zbMATH Open document ID: 0824.17005
author: Alberto Elduque
author: Ivan Shestakov
published in: Journal of Algebra
publication date: 1995-11-15T00:00:00Z
review text: The authors classify the irreducible almost faithful non-Lie modules for a Malcev superalgebra \(M= M_ 0+ M_ 1\) over a ring \(\varphi\) which contains \(1/6\). Let \(V= V_ 0+ V_ 1\) be such a module. There are three cases, loosely described as follows: (1) \(M_ 1= 0\), \(M= M_ 0\) is a simple Lie algebra of dimension 3 over its centroid and \(V\) is a certain module described in the paper. (2) \(M_ 1= 0\), \(M= M_ 0\) is a simple non-Lie Malcev algebra, seven dimensional over its center and \(V\) is the adjoint module. (3) \(M_ 0= 0\), there is a field \(F\) over \(\varphi\) with submodule \(T\) such that \(M_ 1\) is an isomorphic copy of \(T\), \(V_ 0\) and \(V_ 1\) are isomorphic copies of \(F\), the action of \(M\) on \(V\) is described and there is a non-zero element \(y\in F\) such that \(T^ 2 y\) generates \(F\) as a ring.
reviewed by: Ernest L. Stitzinger
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 17D10
zbMATH DE Number: 763964
zbMATH Keywords: irreducible almost faithful non-Lie modules
zbMATH Keywords: Malcev superalgebra
MaRDI profile type: Publication
full work available at URL: jabr.1995.1106
OpenAlex ID: W1985926405
Wikidata QID: Q115396193
DOI: 10.1006/JABR.1995.1106
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description: scientific article; zbMATH DE number 763964