On pseudo-Hermitian quadratic nilpotent Lie algebras. (English) Zbl 07909694
Summary: 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.
MSC:
| 17B30 | Solvable, nilpotent (super)algebras |
| 22E25 | Nilpotent and solvable Lie groups |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
| 53C55 | Global differential geometry of Hermitian and Kählerian manifolds |
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