A Note On The Lie-Amaldi Classification

TL;DR

This paper refines the Lie-Amaldi classification of finite-dimensional nilpotent algebras of vector fields by introducing the rank of the center as a new invariant.

Contribution

It introduces a refinement to the existing classification by incorporating the rank of the center, providing a more detailed invariant for these algebras.

Findings

Refined classification of nilpotent algebras using center rank

Enhanced understanding of algebra structure through new invariant

Potential implications for algebraic and geometric analysis

Abstract

The Lie-Amaldi classification of finite dimensional nilpotent algebras of vector fields is refined, using the rank of the center of the Lie algebra as an invariant.