报告题目：On the solvable Poisson algebras

报 告 人：Bakhrom Omirov

所在单位：Institute for Advances Study of Mathematics, Harbin Institute of Technology

报告时间：2025年6月26日 15:00-15:50

报告地点：禁漫天堂 数学楼第五研讨室

报告摘要: In this talk we present the results on the study of finite-dimensional nilpotent and solvable Poisson algebras. We establish classical results such as Engel’s theorem and Lie’s theorem for Poisson algebras, and examine the role of idempotents in these algebras. The construction of nilpotent and solvable Poisson algebras, exploring the existence of Poisson algebras associated with a fixed Lie algebra, and constructions involving the tensor product and generalized Jacobians will be presented. Furthermore, we show that, under mild restrictions, the solvability and nilpotency of a Poisson algebra are essentially determined by those of the Lie bracket. A criterion for the non-existence of Poisson algebra structures on solvable extensions of nilpotent Lie algebras by a torus will be provided. In particular, we show that complete solvable Lie algebras do not admit a Poisson algebra structure.

报告人简介： 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. He published more than 120 publications.

Bakhrom Omirov is a member of The World Academy of Sciences (TWAS) for the advancement of science in developing countries and were awarded by "Top Researcher in Natural Sciences" Scopus Award (2018), Web of Science Awards in the category of "Highly cited author" (2017) and with the highest state prize of the Republic of Uzbekistan in the field of science and technology (2017).