Graded Lie algebras of maximal class IV

TL;DR

This paper classifies specific infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic, focusing on those generated by elements of weights one and two.

Contribution

It provides a detailed description of the isomorphism classes of these Lie algebras, advancing the understanding of their structure.

Findings

Classification of isomorphism classes achieved

Identification of generators of weights one and two

Clarification of algebra structures in odd characteristic fields

Abstract

We describe the isomorphism classes of certain infinite-dimensional graded Lie algebras of maximal class, generated by an element of weight one and an element of weight two, over fields of odd characteristic.