Research Interests

My research is mainly in Lie Theory and Representation Theory. In particular, I am interested in the following topics:

• Lie (color) algebras
• Lie bialgebras and the classical Yang-Baxter equation
• 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
• Leibniz algebras and Leibniz (co)homology
• Hochschild (co)homology
• Cyclic (co)homology
• Algebraic K-theory
• Invariant theory
• Finite p-groups and associated Lie algebras
• Sporadic simple groups and simple Lie algebras in small characteristics
• Classification of solvable Lie algebras
• Non-associative algebraic structures
• Classification of algebras in low dimensions
• Power sums and related functions
• Plane algebraic curves
• Mathematical foundations of quantum physics
• Geometry and Kinematics of planar mechanisms