Quadratic 2-step Lie algebras: Computational algorithms and classification

TL;DR

This paper introduces a computational method for constructing and classifying quadratic 2-step nilpotent Lie algebras using skew-symmetric matrices, with examples for up to 8 generators.

Contribution

It provides a novel computational approach and classification framework for quadratic 2-step nilpotent Lie algebras based on skew-symmetric matrices.

Findings

Developed an algorithm for constructing these algebras

Classified algebras using families of skew-symmetric matrices

Provided explicit examples for up to 8 generators

Abstract

Taking into account the theoretical results and guidelines given inthis work, we introduce a computational method to construct any 2 step nilpotent quadratic algebra of d generators. Along the work we show that the key of the classification of this class of metric algebras relies on certain families of skewsymmetric matrices. Computational examples for d<=8 will be given.