Title: ON THE UNIQUENESS OF MAXIMAL SOLVABLE EXTENSIONS OF
NILPOTENT LEIBNIZ SUPERALGEBRAS
Speaker: Bakhrom Omirov (National University of Uzbekistan)
Location:数学楼第五研讨室
Time: 16:00-17:00 October 05
Abstract: In this talk, we discuss on the description of maximal solvable extension of complex finite-dimensional nilpotent Leibniz superalgebras under certain conditions. Specifically, we establish that under the condition which ensures the fulfillment of Lie’s theorem for a maximal solvable extension of a special kind of nilpotent Leibniz superalgebra (consistent and d-locally diagonalizable) is decomposed into a semidirect sum of a nilpotent Leibniz superalgebra and a maximal torus on it. In other words, under certain conditions the direct sum of the nilpotent superalgebra and its torus (as a vector spaces), admits a solvable Leibniz superalgebra structure. In addition, for the left-side action of a maximal torus on nilpotent Leibniz superalgebra, which does not admit C^p as a direct summand and is diagonalizable, we prove the uniqueness of the maximal extension. Along with the answer to Snobl’s conjecture for Lie algebras this result covers several already known results for Lie (super)algebras and Leibniz algebras.
Introduction on Bakhrom Omirov:
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).
