Abelian ideals of maximal dimension for solvable Lie algebras

Abstract

We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n less than 8. Furthermore we study the case where there exists an abelian subalgebra of codimension 2. Here we explicitly construct an abelian ideal of codimension 2 in case of nilpotent Lie algebras.

References in corpus (2)

• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra
• On the dimensions of commutative subalgebras and subgroups

Cited by in corpus (9)

• Injective hulls of simple modules over finite dimensional nilpotent complex Lie superalgebras
• Lie solvable enveloping algebras of characteristic two
• The structure of almost Abelian Lie algebras
• Geometric features of Vessiot--Guldberg Lie algebras of conformal and Killing vector fields on ${\mathbb{R}}^2$
• Gaugings of N=4 three dimensional gauged supergravity with exceptional coset manifolds
• The maximal dimension of unital subalgebras of the matrix algebra
• Itô's theorem and metabelian Leibniz algebras
• On abelian subalgebras and ideals of maximal dimension in supersolvable lie algebras
• On a type of commutative algebras