Classification of abelian complex structures on 6-dimensional Lie algebras
Rings and Algebras
2024-07-30 v5 Differential Geometry
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.
Cite
@article{arxiv.0908.3213,
title = {Classification of abelian complex structures on 6-dimensional Lie algebras},
author = {A. Andrada and M. L. Barberis and I. G. Dotti},
journal= {arXiv preprint arXiv:0908.3213},
year = {2024}
}
Comments
v4: The proof of Theorem 3.2 and the statement of Theorem 3.4 have been fixed, and one remark was added. v5: The statement of Theorem 4.4 (assertions (1) and (2)) was fixed and the proof was modified accordingly. Some arguments were clarified