My research is mainly in Lie Theory and Representation Theory. In particular, I am interested in the following topics:
- Lie (color) algebras
- Finite p-groups and associated Lie algebras
- Sporadic simple groups and simple Lie algebras in small characteristics
- Classification of solvable Lie algebras
- Lie coalgebras and Lie comodules
- Lie bialgebras and Lie bimodules
- Lie bialgebras and the classical Yang-Baxter equation
- Leibniz algebras and Leibniz (co)homology
- Hochschild (co)homology
- Cyclic (co)homology
- Quantum groups at roots of unity
- Small quantum groups
- Hopf algebras and the quantum Yang-Baxter equation
- Hopf algebras and tensor categories
- Frobenius algebras
- Clifford algebras
- Hecke algebras
- Cherednik algebras
- Symplectic reflection algebras
- Poisson algebras
- Poisson (co)homology
- Algebraic K-theory
- Invariant theory
- Non-associative algebraic structures
- Classification of algebras in low dimensions
- Power sums and related functions
- Plane algebraic curves
- Geometry and kinematics of planar mechanisms
- Mathematical foundations of quantum physics
- Statistical physics
Subject Areas: Lie theory, representation theory.
