Infinite dimensional analogues of nilpotent and solvable Lie algebras

：Bakhrom Omirov（哈尔滨工业大学）
：2026-01-13 16:30
：海韵园行政楼C503

报告人：Bakhrom Omirov（哈尔滨工业大学）

时  间：2026年1月13日16:30

地  点：海韵园行政楼C503

内容摘要:

The talk is devoted to infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable Lie algebras. We show that classical triangularization results such as Engel's and Lie's theorems are extendable to the pro-setting and establish existence results for the pro-nilpotent radical in pro-solvable algebras and in certain residually solvable algebras. We adapt finite-dimensional construction methods to produce residually solvable extensions with a given pro-nilpotent radical under natural finiteness conditions. By analyzing derivations and maximal tori of pro-nilpotent algebras, we extend the notion of rank and show that, for pro-nilpotent algebras of maximal rank, every derivation of a maximal residually solvable extension is inner. Finally, we describe standard constructions such as tensor products, direct sums, and central extensions, that preserve pro-nilpotency.

个人简介：

Bakhrom Omirov is a professor at the Harbin Institute of Technology, Institute for Advances Study of Mathematics. He graduated Novosibirsk State University (Russia), got his PhD (2002) and Doctor of Sciences (2006) degrees at Institute of Mathematics of Uzbekistan Academy of Sciences. His research focused on solvable Lie and Leibniz (super)algebras, n-Lie algebras and finite-dimensional Poisson algebras.

 

联系人：王清