KTH/SU Mathematics
Colloquium
November 29,
2006
Alexander Stolin,
Chalmers
Towards classification of
quantum groups
ABSTRACT:
In the
fundamental paper "Quantum groups" V.Drinfeld has not defined
explicitly the
notion of a quantum group but he rather explained
it on a number of examples. Later he posed the following
question:
Can any Lie bialgebra be quantized?
A positive answer to the question was obtained by P.Etingof and
D.Kazhdan. This answer
justifies the following definition - 'A semi-classical quantum group
is a quantization of a Lie bialgebra'.
In a recent joint with S.Khoroshkin, A. Pop and V.Tolstoy paper we
posed a conjecture, which refined Drinfeld's problem above. Namely,
Can any classical twist be quantized?
The latter problem was recently solved by G. Halbout in his paper
"Formality theorem for Lie algebras and quantization of twists
and coboundary r-matrices" (to appear in Adv. Math. December 2006).
This result gives a basis for classification of quantum groups.