报告人:Bakhrom Omirov
报告地点:数学与统计学院317
报告时间:2024年10月05日星期六09:00-10:00
邀请人:陈良云、刘杰锋
报告摘要:
In this talk we shall discuss on the description of some maximal solvable extensions of nilpotent Lie superalgebras. Namely, we show that under a condition ensuring the fulfillment of an analogue of Lie's theorem, the maximal solvable extension of a d-locally diagonalizable nilpotent Lie (super)algebra can be decomposed into a semidirect sum of its nilradical and the maximal torus of the nilradical. In the case of Lie algebras, this result provides an answer to Snoble's conjecture. We present an alternative method for describing the above-mentioned solvable Lie (super)algebras. In addition, we establish a criterion for the completeness of solvable Lie algebras and prove that the first cohomology group with coefficient itself for a solvable Lie algebra vanishes if and only if it is a maximal solvable extension of a d-locally diagonalizable nilpotent Lie algebra. Finally, we give an example illustrating that the result obtained for describing maximal solvable extensions of nilpotent Lie (super)algebras is not true for Leibniz algebras.
主讲人简介:
Bakhrom Omirov is a professor at the National University of Uzbekistan. His research focused on non-associative algebras and superalgebras. In particular, he is one of the authors of the monograph devoted to the structure theory of Leibniz algebras. Bakhrom Omirov is a member of The World Academy of Sciences, which includes 66 countries), as well as Uzbek and American Societies.
He is a winner of several prestigious fellowships (Fulbright, USA; INTAS, Belgium).