Cartan Subalgebras, Weight Spaces, and Criterion of Solvability of Finite Dimensional Leibniz Algebras

Abstract

In this work the properties of Cartan subalgebras and weight spaces of finite dimensional Lie algebras are extended to the case of Leibniz algebras. Namely, the relation between Cartan subalgebras and regular elements are described, also an analogue of Cartan’s criterion of solvability is proved.