Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ,
Keywords: Lie algebras; representations of Lie algebras; cohomology of Lie algebras; algebraic groups.
Subject:
The classification of simple 1-graded Lie algebras with various components $L_0$ under weak restriction on the characteristic of the ground field was obtained. The integrable distributions over the truncated polynomial algebra were investigated. The theory of truncated induced and coinduced modules over the transitive Lie algebras of characteristic p is constructed. The theorems on the minimal imbedding of a transitive Lie algebra into the general Lie algebra of Cartan type are proved. The exceptional modules over the filtered Lie algebras of Cartan type are investigated. A new method of finding the geometrical realizations of bitransitive graded Lie algebras was developed. The geometrical realization of Melikyan algebras was obtained. A new method of defining systems of functions for finding the maximal tori in p-closure of a transitive Lie algebra was developed. A number of papers (with N. G. Chebochko) were devoted to the study of deformations of classical Lie algebras of small characteristics. The deformations, automorphisms (with O. A. Mulyar) and derivations of Melikyan algebras and other Lie algebras admitting the geometrical realization were investigated.
Main publications:
The Melikyan algebras as Lie algebras of the type $G_2$ // Commun. Algebra, 1991, 19(4), 1281–1312.
Classification of simple 1-graded Lie algebras of characteristic $p$ // Contemp. Math., 1995, 184, 255–265.
