Research
Quantum groups, Hopf algebras, and quantization of G-spaces.
My research area is quantum groups, Hopf algebras, and quantization of G-spaces. This is a part of non-commutative algebra for which quantum integrable models being the source of motivation and problems. My primary research interests currently lie in equivariant quantization of G-spaces. Given a Poisson group G and a Poisson G-space M, the problem to construct an associative deformation of the function algebra F(M) and homogeneous vector bundles over M as its projective (one-sided) modules. The deformation is assumed to preserve an action of the quantum group corresponding to G.
Among my strongest achievments are explicit quantization of semisimple conjugacy classes of simple complex algebraic groups, the theory of dynamical Yang-Baxter equation over general non-Abelian, base and a partial solution of Drinfeld's problem about relation of quasi-Hopf algebras and quantized Poisson-Lie manifolds.
