A Class of Solvable Lie Algebras and Their Hom-Lie Algebra Structures

The finite-dimensional indecomposable solvable Lie algebras s with Q2n+1as their nilradical are studied and classified, it turns out that the dimension of s is dim Q2n+1+1.Then the Hom-Lie algebra structures on solvable Lie algebras s are calculated.

Solvable Lie Algebras with Nilradical Q_(2n+1) and Their Casimir Invariants

The finite-dimensional indecomposable solvable Lie algebras s with Q_(2n+1) as their nilradical are studied and classified and their Casimir invariants are calculated. It turns out that the dimension of s is at most dim Q_(2n+1)+2.

The isomorphic realization of nondegenerate solvable Lie algebras of maximal rank based on Kac-Moody algebras

In this paper,based on Kac-Moody algebra,the isomorphic realization of nondegenerate solvable Lie algebras of maximal rank is given,which in turn revels the closed connections between nondegenerate solvable Lie algebras and Kac-Moody algebras,resulting in some new worthy topics in this area.

Solvable complete Lie algebras (I)

Let N be a nilpotent Lie algebra. An abelian subalgebra of DerN, whose elements are semisimple linear transformations of N, is called a torus on N. The dimension of a maximal torus H on N is called the rank of N.

Oriented Tree Diagram Lie Algebras and Their Abelian Ideals

We introduce oriented tree diagram Lie algebras which are generalized from Xu＇s both upward and downward tree diagram Lie algebras, and study certain numerical invariants of these algebras related to abelian ideals.