On abelian subalgebras and ideals of maximal dimension in supersolvable lie algebras

Details On abelian subalgebras and ideals of maximal dimension in supersolvable lie algebras On abelian subalgebras and ideals of maximal dimension in supersolvable lie algebras

2011-10-11

arxiv.org/abs/1110.2389v1

Mathematics

Rings and Algebras

Scientific paper

In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codimension 2. Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of codimension 3 contain an abelian ideal with the same dimension, provided that the characteristic of the underlying field is not two. Throughout the paper, we also give several examples to clarify some results.

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