On Nilpotent Leibniz Algebras and Their Derivations

[Math. Dept.]

March 14, 2018  16:00-17:00

W303  School of Mathematics

[colloquium] Bakhrom Omirov20180314-01.png

 SPEAKER

Bakhrom Omirov (National University of Uzbekistan)

 ABSTRCT

Leibniz algebras are generalizations of Lie algebras and they have been introduced by J.-L. Loday as a non-antisymmetric version of Lie algebras. These algebras preserve a unique property of Lie algebras - the right multiplication operators are derivations. Many classical results of the theory of Lie algebras were extended to the case of Leibniz algebras. For instance, the analogue of Levi's theorem for Leibniz algebras is also true. Namely, it is proved that any finite-dimensional Leibniz algebra is decomposed into the semidirect sum of solvable radical and semisimple Lie subalgebra. Therefore, the biggest challenge in the classification problem of finite-dimensional Leibniz algebras is the study of solvable part. The method of the description of solvable Lie algebras with a given nilradical which involve outer derivations of a nilreadical was extended to the case of Leibniz algebras. Therefore, the problem of classification of finite-dimensional Leibniz algebras reduces to study of nilpotent one and their derivations. In this talk we are going to present results on nilpotent Leibniz algebras and their derivations.case of Leibniz algebras. Therefore, the problem of classification of finite-dimensional Leibniz algebras reduces to study of nilpotent one and their derivations. In this talk we are going to present results on nilpotent Leibniz algebras and their derivations.

 SUPPORTED BY

School of Mathematics, Sichuan University