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On maximal subalgebras of central simple Malcev algebras. (English) Zbl 0592.17014

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.
Reviewer: E.L.Stitzinger

MSC:

17D10 Mal’tsev rings and algebras
17A30 Nonassociative algebras satisfying other identities
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References:

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