Real non-degenerate two-step nilpotent Lie algebras of dimension eight

TL;DR

This paper classifies all real non-degenerate two-step nilpotent Lie algebras of dimension eight, providing explicit structure constants by leveraging known complex cases.

Contribution

It offers a complete classification of these Lie algebras over the real numbers, including explicit structure constants, extending previous complex classifications.

Findings

Complete classification of 8-dimensional real non-degenerate two-step nilpotent Lie algebras.

Explicit structure constants for each classified algebra.

Extension of complex classification results to the real case.

Abstract

We classify the non-degenerate two-step nilpotent Lie algebras of dimension 8 over the field of real numbers, using known results over complex numbers. We write explicit structure constants for these real Lie algebras.