Multibracket simple Lie algebras

TL;DR

This paper introduces higher-order multibracket simple Lie algebras, generalizing traditional Lie algebras using cohomology cocycles, and develops a nilpotent BRST operator for these structures.

Contribution

It presents a novel class of multibracket simple Lie algebras based on Lie algebra cohomology and constructs a corresponding nilpotent BRST operator.

Findings

Definition of multibracket simple Lie algebras

Use of Lie algebra cohomology cocycles for structure constants

Construction of a nilpotent, complete BRST operator

Abstract

We introduce higher-order (or multibracket) simple Lie algebras that generalize the ordinary Lie algebras. Their `structure constants' are given by Lie algebra cohomology cocycles which, by virtue of being such, satisfy a suitable generalization of the Jacobi identity. Finally, we introduce a nilpotent, complete BRST operator associated with the l multibracket algebras which are based on a given simple Lie algebra of rank l.