Report Title：Local derivations and automorphisms on solvable Lie algebras of maximal rank

Reporter: Bakhrom Omirov

Institution：National University of Uzbekistan

Time：November 18,2022  10:30-12:30

Location：ZOOM ID：862 062 0549，Code：2022

Meeting link：//us02web.zoom.us/j/8620620549?pwd=bGhsaG15WjRza2V3ZEN4TzJYZ1FZQT09

Abstract：The present talk is devoted to the description of local derivations and automorphisms on solvable Lie algebras of maximal rank. First, we present the general form of an automorphism on solvable Lie algebra of maximal rank. Namely, any automorphism can be represented as a composition of inner, diagonal and graph automorphisms. We show that all local derivations and all local automorphisms of solvable Lie algebra of maximal rank are global, while there are examples of solvable Lie algebras of non-maximum rank with different behavior of local derivations and local automorphisms. We also apply the main results to the descriptions of local derivations and local automorphisms on standard Borel subalgebras of complex simple Lie algebras.

Introduction of the Reporter：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).