About a family of naturally graded no p-filiform Lie algebras

Abstract

The knowledge of the naturally graded algebras of a given class of Lie algebras offers essential information about the structure of the class. So far, the classification of naturally graded Lie algebras is only known for some families of p-filiform Lie algebras. In certain sense, if 𝖌 is a naturally graded Lie algebra of dimension 𝑛, the first case of no 𝑝-filiform Lie algebras it happens when the characteristic sequence is (𝑛 − 3, 2, 1). We present the classification of a particular family of these algebras with finite arbitrary di- mension, when the dimension of the derived ideal is minimum. The use of the package Mathematica 4 has been essential in order to obtain the results.