Grant: Discovery Grants Program - Individual

My research area 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 including knot and braid theory, operator algebras, quantum theory and statistical mechanics. They 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. 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 objects in an appropriate category associated to a Hopf algebra. Objects of this kind include so-called colour Lie superalgebras, which arose in particle physics. The proposed research deals with classical objects of mathematics such as matrix algebras and finite-dimensional simple Lie (super)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.