Structure Constant Formulas for the Universal Enveloping Algebras of the Nilpotent Lie Algebras of Dimension Five and Less

TL;DR

This paper derives explicit structure constant formulas for the universal enveloping algebras of all nilpotent Lie algebras of dimension five or less, based on a classification of small-dimensional Lie algebras.

Contribution

It provides the first comprehensive formulas for these universal enveloping algebras, extending previous classifications to explicit algebraic structures.

Findings

Explicit structure constant formulas for nilpotent Lie algebras of dimension ≤5

Complete classification of these algebras used as a foundation

Facilitates further algebraic and representation-theoretic studies

Abstract

Libor \v{S}nobl and Pavel Winternitz classified all of the Lie algebras of dimension six and smaller. Using this classification, we formulated and proved structure constant formulas for the universal enveloping algebras of the nilpotent Lie algebras of dimension five and less.