(TLie)-Leibniz algebras and related properties

Abstract

In [6], it is studied properties of the class D Lie of non-perfect Leibniz algebras with non-trivial Lie-centers. In this paper, we study properties of Leibniz algebras of class T Lie , a subclass of both the class D Lie and the class of Lie-stem Leibniz algebras. We determine necessary and sufficient conditions under which a non-Lie Leibniz algebra is of class T Lie and study their relationship with pseudo-abelian Leibniz algebras. We also show that Leibniz algebras of class T Lie have semi-simple central Lie-derivations.