Report Title：On Some Constructions of n-Lie Algebras
Reporter：Bakhrom Omirov
Affiliation:Institute for Advances Study of Mathematics, Harbin Institute of Technology
Report Time: September 15, 2026, 15:00–17:00
Report Location: Room 209, Zhengxin Building
Abstract:
We study constructions of n-Lie algebras, with particular attention to infinite-dimensional simple examples. First, we investigate Pozhidaev’s algebras using equivariant bilinear maps, 1/n-derivations, and inner derivation algebras. These invariants distinguish them from the full algebras arising from the standard S, W and SW constructions. We also describe realizations through derived subalgebras and central quotients, clarifying the scope of this distinction.
Next, we consider determinant brackets defined by commuting derivations and additional columns of algebra elements. Using complementary minors and Grassmann–Plücker relations, we obtain an explicit criterion for these brackets to define n-Lie structures and illustrate it with concrete examples. Finally, we discuss tensor products and quotient constructions relating ordinary algebras to n-Lie algebras.
This talk is based on joint work with Xinru Cao and Zafar Normatov.
Bio:
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).
