The Variety of Lie algebras of maximal class

TL;DR

This paper explicitly describes the algebraic variety of Lie algebras of maximal class, providing polynomial equations that define this space, which is crucial for understanding their deformations.

Contribution

It offers the first explicit polynomial equations for the affine variety of maximal class Lie algebras, advancing the classification and deformation theory of these structures.

Findings

Explicit polynomial equations for the variety are derived.

The variety serves as the base for nilpotent versal deformations.

Provides a foundation for further classification of filiform Lie algebras.

Abstract

We present an explicit description of the affine variety of Lie algebras of the maximal class (filiform Lie algebras): the formulas of polynomial equations that determine this variety are written. It can considered as the base of the nilpotent versal deformation of N-graded Lie algebra m_0.