On n-maximal subalgebras of Lie algebras

2015/02/10 by David A. Towers, Towers, David A.
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA) #math.GR #math.RA

paper · pdf · doi:10.48550/arxiv.1502.02865

arxiv created 2015/02/10 · arxiv updated 2015/02/11

Abstract

A chain S₀ < S₁ < … < S_n = L is a \em maximal chain if each S_i is a maximal subalgebra of S_i+1. The subalgebra S₀ in such a series is called an \em n-maximal subalgebra. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra L imply about the structure of L itself. Here we consider whether similar results can be obtained by imposing conditions on the n-maximal subalgebras of L, where n>1.

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