My reseach interests are in mathematical physics and algebra. In particular,
I am interested in quantum groups and differential calculus on quantum
groups and quantum spaces. Quantum groups generalize the concept of Lie
groups and universal enveloping algebras of Lie algebras. The first interesting
examples of quantum groups were developed by Drinfeld, Jimbo, Manin,
and Woronowicz in the mid 1980s. The quantum group SLq(2)
is a deformation of the (commutative) ring of regular functions on the
group SL(2). The group structure is reflected in the Hopf algebra structure
of SLq(2). Nowadays, almost all simple Lie groups
have one ore more quantum analogues. Quantum spaces generalize the
concept of homogeneous spaces.
It is commonly expected that quantum groups will provide new
ideas and technics to solve fundamental problems in mathematical
physics as the connection of quantum theory and gravitation and the quantum
structure of space time at the Planck scale.