On pseudo-Hermitian quadratic nilpotent Lie algebras
Rings and Algebras
2023-01-18 v1 Differential Geometry
Abstract
We study nilpotent Lie algebras endowed with a complex structure and a quadratic structure which is pseudo-Hermitian for the given complex structure. We propose several methods to construct such Lie algebras and describe a method of double extension by planes to get an inductive description of all of them. As an application, we give a complete classification of nilpotent quadratic Lie algebras where the metric is Lorentz-Hermitian and we fully classify all nilpotent pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian metrics.
Keywords
Cite
@article{arxiv.2301.06462,
title = {On pseudo-Hermitian quadratic nilpotent Lie algebras},
author = {Mustapha Bachaou and Ignacio Bajo and Mohamed Louzari},
journal= {arXiv preprint arXiv:2301.06462},
year = {2023}
}