On Graded Deformations of The universal Enveloping Algebra of a Color Lie Algebra

TL;DR

This paper introduces the concept of graded deformations for the universal enveloping algebra of a color Lie algebra and provides explicit examples of such deformations.

Contribution

It defines graded deformations in the context of color Lie algebras and constructs explicit graded deformations of their universal enveloping algebras.

Findings

Explicit graded deformations are constructed for the universal enveloping algebra.

The notion of graded deformation is formalized for color Lie algebras.

Provides a framework for future deformation studies in algebraic structures.

Abstract

Let $\mathfrak{g}$ be a Color Lie Algebra and $\mathcal{U}(\mathfrak{g})$ its the universal Enveloping Algebra. We define the notion of graded deformations and we give explicit graded deformations of the universal Enveloping Algebra of $\mathfrak{g}$.