A class of Lie algebras who contains a class of Kac-Moody algebras

TL;DR

This paper introduces PC Lie algebras, a new class of Lie algebras constructed via standard pentads, and demonstrates that they encompass Kac-Moody algebras, extending their framework.

Contribution

It shows that PC Lie algebras form a broader class that includes Kac-Moody algebras, extending the existing theory of Lie algebra constructions.

Findings

PC Lie algebras contain Kac-Moody algebras

Standard pentads enable embedding Lie algebras into graded structures

The class of PC Lie algebras extends Kac-Moody algebra framework

Abstract

The theory of standard pentads is the theory aims to construct a graded Lie algebra whose local part consists of a given Lie algebra and its representation. In other words, using standard pentads, we can embed given Lie algebra and its representation into a larger graded Lie algebra. As special cases of Lie algebras associated with standard pentads, we have the notion of PC Lie algebras. Our aim of this paper is to show that the class of PC Lie algebras contains the class of Kac-Moody algebras, that is, to show that the notion of PC Lie algebras is an extension of Kac-Moody algebras.