The Computation of Abelian Subalgebras in Low-Dimensional Solvable Lie Algebras

The main goal of this paper is to compute the maximal abelian dimension of each solvable nondecomposable Lie algebra of dimension less than 7. To do it, we apply an algorithmic method which goes ruling out non-valid maximal abelian dimensions until obtaining its exact value. Based on Mubarakzyanov and Turkowsky’s classical classifications of solvable Lie algebras (see [13] and [19]) and the classification of 6-dimensional nilpotent Lie algebras by Goze and Khakimdjanov [7], we have explicitly computed the maximal abelian dimension for the algebras given in those classifications. Key–Words: Solvable Lie algebra, maximal abelian dimension.