This repository includes my work from Oct 2023 - June 2024 on Universal Enveloping Algebras and the PBW Theorem, guided by Prof. Haynes Miller of MIT.
The attached PDF includes the mathematical progress made outside of my work on https://arxiv.org/abs/2309.07962 (which I co-authored). It consists of an analysis of universal enveloping algebras from the perspective of relations, examples of them, and some discussion regarding PBW theorems.
The attached .ipynb file contains my code for calculating a Grobner basis for determining a universal enveloping algebra. Instructions are contained in the file if one wishes to recreate my work. They are contained in "####" blocks.