Title：Nilpotent Lie algebras with quadratic pseudo-Hermitian metrics

Reporter：Ignacio Bajo

Work Unit：Universidad de Vigo (Spain)

Time：2023/10/26 20:00-22:00

Address：Zoom id：904 645 6677 Password:2023

**Summary of the report: **

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 use a method of double extension by planes to get an inductive description of all of them. Such a method let us give a complete classification of nilpotent quadratic Lie algebras where the metric is Lorentz-Hermitian and to obtain a complete classification of pseudo-Hermitian quadratic Lie algebras up to dimension 8 and their inequivalent pseudo-Hermitian metrics.

**Introduction of the Reporter: **

Ignacio Bajo works at the Departament of Applied Mathematics II in the University of Vigo and currently the Chair of the Department. His research interests nowadays are focused on Lie algebras and Lie groups but also on other non-associative algebras related to geometrical problems.