Abelian subalgebras in some particular types of Lie algebras

It is well-known that there exists a close link between Lie Theory and Relativity Theory. Indeed, the set of all symmetries of the metric in our four-dimensional spacetime is a Lie group. In this paper we try to study this link in depth, by dealing with three particular types of Lie algebras: hn algebras, gn algebras and Heisenberg algebras. Our main goal is to compute the maximal abelian dimensions of each of them, which will allow us to move a step forward in the advancement of this subject.