Lie algebras and extremal elements

An L Lie algebra is defined as a vector space with a transformation that provides bilinear, skew-symmetric and Jacobi identity on field F. For each y∈L, the elements x∈L that provide the condition [x,[x,y]] ∈Fx are called extremal elements. In this study, the center, central and inner automorphisms of Lie algebras generated by two and three extremal elements and the normalization of some subspaces were investigated.