Grant: Discovery Grants Program - Individual

My area of interest is the theory of Hopf agebras and its connections to noncommutative ring theory and Lie theory. Hopf algebras arise in many areas of mathematics and theoretical physics (knot and braid theory, operator algebras, quantum theory, statistical mechanics - to name a few) and provide a new unified approach to many classical problems in algebra. There have been impressive recent advances in this field. The focus of the proposed research program will be on actions (or coactions) of Hopf algebras on other algebras (associative, Lie, etc.). In particular, the theory of Hopf algebras gives a unified approach to the study of graded algebras, algebras with automorphisms, and algebras with derivations by viewing them as algebras in the category of (co)modules over an appropriate Hopf algebra. Another promising direction of research in this area is the Lie-theoretical aspects of the theory of Hopf algebras, which have not yet been sufficiently investigated. The proposed research deals with classical objects of mathematics such as matrix algebras and finite-dimensional simple Lie algebras and is expected to contribute to the advancement of knowledge in fundamental areas of algebra. It may also find applications in other areas of mathematics and in theoretical physics.