Title: On Solvable Poisson Algebras
Speaker: Prof. Bakhrom Omirov
Affiliation: Institute for Advanced Study of Mathematics, Harbin Institute of Technology
Time: 15:00-15:50, June 26, 2025
Location: Seminar Room 5, Mathematics Building, Jilin University
Abstract:
This presentation will showcase our latest findings on finite-dimensional nilpotent and solvable Poisson algebras. We will demonstrate classical theorems including Engel's theorem and Lie's theorem in the context of Poisson algebras, while analyzing the significance of idempotent elements within these algebraic structures. Key aspects to be addressed include:
Methodologies for constructing nilpotent and solvable Poisson algebras
Investigations into the existence of Poisson algebras corresponding to given Lie algebras
Innovative construction approaches utilizing tensor products and generalized Jacobians
Our research reveals that, subject to reasonable constraints, both the solvability and nilpotency properties of a Poisson algebra are fundamentally governed by its underlying Lie bracket structure. We will introduce a decisive criterion regarding the impossibility of establishing Poisson algebra structures on solvable extensions of nilpotent Lie algebras via tori, with the particularly significant result that complete solvable Lie algebras cannot support Poisson algebra structures.
Speaker's Biography:
Prof. Bakhrom Omirov currently holds a professorship at the Institute for Advanced Study of Mathematics, Harbin Institute of Technology. An alumnus of Novosibirsk State University (Russia), he obtained his PhD (2002) and Doctor of Sciences (2006) degrees from the Institute of Mathematics at the Uzbekistan Academy of Sciences. His distinguished research career has concentrated on solvable Lie algebras, Leibniz (super)algebras, n-Lie algebras, and finite-dimensional Poisson algebras, culminating in over 120 scholarly publications.
Prof. Omirov has been elected as a Fellow of The World Academy of Sciences (TWAS), recognizing his contributions to scientific advancement in developing nations. His numerous accolades include:
The prestigious "Top Researcher in Natural Sciences" Scopus Award (2018)
Web of Science's "Highly Cited Author" distinction (2017)
The Republic of Uzbekistan's highest honor in science and technology (2017)
