In this paper we investigate the existence of invariant SKT, balanced and generalized Kähler structures on compact quotients Γ﹨G, where G is an almost nilpotent Lie group whose nilradical has one-dimensional commutator Γ a lattice G. We first obtain characterization Hermitian algebras g n classification result in real dimension six. Then, study ones admitting SKT examine behaviour such under fl...

A flat solvmanifold is a compact quotient $$\Gamma \backslash G$$ where G simply-connected solvable Lie group endowed with left invariant metric and $$ lattice of G. Any such can be written as $$G={\mathbb {R}}^k < imes _{\phi } {\mathbb {R}}^m$$ $${\mathbb the nilradical. In this article we focus on 6-dimensional splittable solvmanifolds, which are obtained quotienting by that decomposed =\Gam...

This work is devoted to the study of central extensions some solvable Leibniz superalgebras. We show that a superalgebra with non-null center can be obtained by extension other ones lower dimensions. Moreover, we describe for maximal Lie superalgebras nilradical which neither characteristically nilpotent in non-split case nor do not involve as term split case. Additionally, apply two different ...

This paper studies the canonical symmetric connection $\nabla$ associated to any Lie group $G$. The salient properties of are stated and proved. symmetries geodesic system a general linear formulated. results then applied in special case where algebra $\g$ $G$, has codimension one abelian nilradical. conditions that determine symmetry such completely integrated. Finally obtained compared with s...