Ivan Kaygorodov

• Abstract

  The project is dedicated by the study of Leibniz and Novikov algebras. The main goal is to find algebraic and geometric classifications of low-dimensional Novikov algebras and study irreducible components and rigid algebras in varieties of Novikov and Leibniz algebras of dimension n. (AU)

  The geometric classification of non-assocociative algebras, AV.EXT

• Abstract

  The project is dedicated by the study of representation theory for enveloping algebras of nilpotent Leibniz algebras. The main goal is to establish an analogue of the orbit method for such algebras and to describe their primitive ideals. (AU)

  Enveloping algebras of nilpotent Leibniz algebras, AV.EXT

• Abstract

  The main objects are Lie algebras and Leibniz algebras, which are the main classes of non-associative algebras. The typical questions in this line deal with the study of general derivations of simple and semisimple algebras. (AU)

  Generalized derivations of non associative algebras, AV.BR

(Only some records are available in English at this moment)

• Abstract

  The research project is for the post-doc program in algebra. Derivations, automorphisms, an analog of the Bergman Centralized Theorem and analogs of Makar-Limanov's results for free Poisson algebras will be considered for free general (non-Lie-admissible) Poisson algebra. Also, the algebras of delta-derivations of some simple finite-dimensional Filippov algebras and ternary Malcev algebra…

  General Poisson algebras and generalized derivarions, BP.PD

• Abstract

  The project will be dedicated to gradings of algebras. The main objects are conservative algebras, Fillipov (n-Lie) and n-ary Leibniz algebras. The typical questions of this line are the study of the structure of n-algebras graded and split algebras. Another part of the project will be devoted to describing possible gradings in simple algebras and superalgebras. (AU)

  Graded structures, BE.PQ

• Abstract

  The project will be devoted to n-ary algebras. The main objects are Fillipov algebras (n-Lie) and Leibniz n-ary algebras. The typical questions in this line are the study of the structure of split n-ary algebras and the structure of algebras with a multiplicative and quasi-multiplicative base. (AU)

  N-ary split strutures, BE.PQ