Title：On pseudo-Euclidean Lie algebras whose Levi-Civita product is left Leibniz

Reporter：Said Benayadi

School：University of Lorraine-Metz

Report time：2023年3月30日 20:00-22:00

Report to ZOOM Id：ZOOM Id：904 645 6677，Password：2023

Conference link：https://us02web.zoom.us/j/9046456677?pwd=UHErd3RJVzFsNzNnczFZYm9uYlV6QT09

Summary of report: We study a class of Lie algebras which contains the class of quadratic Lie algebras and the class of Milnor Lie algebras, namely, Lie algebras endowed a pseudo-Euclidean metric such its Levi- Civita product is left Leibniz. We call them Levi-Civita left Leibniz Lie algebras LCLL for short. We show that a Lie group (G, h) endowed with a left invariant pseudo-Riemannian such that the corresponding Lie algebra is LCLL is complete and locally symmetric. Moreover, we prove that any Euclidean LCLL Lie algebra is the product of quadratic a Lie algebra and a flat Euclidean Lie algebra. We develop an adapted version of the process of double extension to construct LCLL Lie algebras. We show that Lorentzian or flat LCLL Lie algebras can be obtained by this process.

Brief introduction of reporter：Said Benayadi is a professor in University of Lorraine-Metz. His research interest is nonassociative algebras.