Representations$^{6-th}$ of Lie Algebras

TL;DR

This paper introduces a new concept called representations$^{6-th}$ of Lie algebras and explores their algebraic properties, including analogs of classical theorems and structures.

Contribution

It defines representations$^{6-th}$ of Lie algebras and investigates their associated P-B-W Theorem and Hopf algebra structures, extending classical Lie algebra theory.

Findings

Established the concept of representations$^{6-th}$ of Lie algebras.

Derived the P-B-W Theorem for these representations.

Analyzed the Hopf algebra structure in this context.

Abstract

We introduce representations$^{6-th}$ of Lie algebras, and study the counterparts of the P-B-W Theorem and the Hopf algebra structure for the enveloping algebras of Lie algebras in the context of representations$^{6-th}$ of Lie algebras.