Structures, representations, and applications of algebraic systems

Abstract

Most of the project will be dedicated to Lie and Jordan algebras and superalgebras and their representations. In addition, Malcev and alternative algebras and superalgebras will be considered, Moufang loops and various generalizations and applications of above. Algebraic systems related to integrable systems of differential equations will be considered. Homological methods will be applied in the theory of representations and finely presentable algebraic structures. The lines of the research project focus on the following themes: representations of Lie algebras and superalgebras; structural questions for representations of related Kac-Moody algebras and their generalizations; non-associative algebras, their applications and generalizations; representations of Lie and Jordan superalgebras, application of Tits-Kantor-Koecher construction free Jordan algebra; combinatorial theory of algebras; theory of loops, their relations and applications; integrable systems and non-associative structures; representations of algebras: homological and geometric methods; finitely presentable and homological type FP-m structures. (AU)