Classification of integrable complex structures on 6-dimensional product Lie algebras

TL;DR

This paper classifies all integrable complex structures on 6-dimensional Lie algebras formed by the product of a Lie algebra with itself, providing a comprehensive understanding of their complex structures.

Contribution

It offers a complete classification of integrable complex structures specifically on 6-dimensional product Lie algebras, a previously unexplored area.

Findings

Complete classification of integrable complex structures on these Lie algebras

Identification of structural properties enabling integrability

Framework for analyzing complex structures on product Lie algebras

Abstract

We classify all integrable complex structures on 6-dimensional Lie algebras of the form $\mathfrak{g}\times\mathfrak{g}$.