On complemented non-abelian chief factors of a Lie algebra

2015/09/24 by David A. Towers, Towers, David A., Zekiye Ciloglu +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.GR #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1509.07282

arxiv created 2015/09/24 · arxiv updated 2015/09/25

Abstract

The number of Frattini chief factors or of chief factors which are complemented by a maximal subalgebra of a finite-dimensional Lie algebra L is the same in every chief series for L, by \cite[Theorem 2.3][11]. However, this is not the case for the number of chief factors which are simply complemented in L. In this paper we determine the possible variation in that number.

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