SPEAKER: Arkady Berenstein

TITLE: Braided Doubles and rational Cherednik algebras.

ABSTRACT: In my talk (based on a recent joint paper with Yuri Bazlov) I
will introduce a general class of algebras

with triangular decomposition which we call "braided doubles". Braided
doubles provide a unifying framework

for all classical and quantum universal enveloping algebras and
recently discovered rational Cherednik algebras.

Quite surprisingly, one can completely classify free braided doubles.

The classification is achieved in terms of Yetter-Drinfeld (YD-)modules
over Hopf algebras and their genralizations.

In particular, to each R-matrix one associates a canonical YD-module so
that the corresponding braided double U(R)

is a deformation of the Weyl algebra, where the role of polynomial
algebras is played by Nichols-Woronowicz algebras.

The main result is that any rational Cherednik algebra canonically
embeds into the double U(R) attached to the

R-matrix emerging from each complex reflection group. This embedding
gives a new definition of

rational Cherednik algebras and the instantaneous proof of their
triangular decomposition.