On Free Pseudo-Product Fundamental Graded Lie Algebras

TL;DR

This paper classifies the prolongations of complex free fundamental graded Lie algebras, introduces free pseudo-product variants, and studies their automorphism groups, advancing the understanding of their structure and symmetries.

Contribution

It provides a classification of prolongations for free fundamental graded Lie algebras and introduces the concept of free pseudo-product variants with analysis of their automorphisms.

Findings

Classification of prolongations of complex free fundamental graded Lie algebras

Introduction of free pseudo-product fundamental graded Lie algebras

Analysis of automorphism groups of these prolongations

Abstract

In this paper we first state the classification of the prolongations of complex free fundamental graded Lie algebras. Next we introduce the notion of free pseudo-product fundamental graded Lie algebras and study the prolongations of complex free pseudo-product fundamental graded Lie algebras. Furthermore we investigate the automorphism group of the prolongation of complex free pseudo-product fundamental graded Lie algebras.