Index of Graded Filiform and Quasi Filiform Lie Algebras

TL;DR

This paper computes the index and identifies regular vectors for graded filiform and quasi-filiform nilpotent Lie algebras, focusing on specific classes and dimensions to deepen understanding of their algebraic structure.

Contribution

It provides explicit index calculations and regular vectors for various classes of graded filiform and quasi-filiform Lie algebras, including low-dimensional cases.

Findings

Index values for graded filiform Lie algebras $L_{n}$ and $Q_{n}$ for $n<8$

Index and regular vectors for graded quasi-filiform Lie algebras

Analysis of Lie algebras with nilradical $Q_{2n}$

Abstract

The filiform and the quasi-filiform Lie algebras form a special class of nilpotent Lie algebras. The aim of this paper is to compute the index and provide regular vectors of this two class of nilpotent Lie algebras. we consider the graded filiform Lie algebras $L_{n}$, $Q_{n}$, the $n$-dimensional filiform Lie algebras for $n$ $<8$, also the graded quasi-filiform Lie algebras and finally Lie algebras whose nilradical is $Q_{2n}$.