On maximal subalgebras of central simple Malcev algebras
type: Item
instance of: scholarly article
title: On maximal subalgebras of central simple Malcev algebras
zbMATH Open document ID: 0592.17014
DOI: 10.1016/0021-8693(86)90181-X
author: Alberto Elduque
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let A be a central simple non-Lie Malcev algebra over a field F of characteristic not 2. It is recalled that A is forced to be finite dimensional, \(\dim (A)=7\) and particular kinds of multiplication tables for A exist. The author determines the maximal subalgebras M of A. There are exactly two types, depending on what type of Cartan subalgebra C of A exists in M. If C is split, then \(\dim (M)=5\) and M is isomorphic to \(V+S\) where \(VS=V\), \(VV=0\), \(S\cong sl(2,F)\) and V is a certain type of S-module. If no C in M is split, then \(\dim (M)=3\) and M is a non-split simple Lie algebra.
Mathematics Subject Classification ID: 17D10
Mathematics Subject Classification ID: 17A30
zbMATH DE Number: 3950779
zbMATH Keywords: characteristic not two
zbMATH Keywords: non-Lie Malcev algebra
zbMATH Keywords: maximal subalgebras
reviewed by: Ernest L. Stitzinger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3950779