Research Interests

Lie algebras | Malcev algebras | Jordan algebras | Superalgebras | Group gradings

Generally, I am interested in various nonassociative structures/algebras such as Lie, Jordan and Malcev algebras, superalgebras and triple systems (LTS, JTS, GJTS, etc.). The study of nonassociative algebras began back in 19th century when 8-dimensional octonion algebra (also known as Cayley-Dickson algebra) was discovered. Today the theory of nonassociative algebras is a well developed area of mathematics with many applications and unsolved questions. One of the open problems is the classification of nilpotent Lie algebras.
Currently, my research focus is on studying filiform Lie algebras, a subclass of nilpotent Lie algebras. Generalization of this concept to the infinite-dimensional case is so-called a Lie algebra of maximal class. The main open problem is to classify these algebras up to an isomorphism.