Classification of abelian complex structures on 6-dimensional Lie algebras

TL;DR

This paper classifies 6-dimensional Lie algebras that admit abelian complex structures and describes the space of these structures up to holomorphic isomorphism, providing a comprehensive understanding of their geometric properties.

Contribution

It provides a complete classification of abelian complex structures on 6-dimensional Lie algebras and parametrizes these structures up to holomorphic isomorphism, a novel contribution in the field.

Findings

Complete classification of 6-dimensional Lie algebras with abelian complex structures

Parameterization of the space of such structures

Identification of isomorphism classes

Abstract

We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.