Fabio Gavarini
Quantization of Poisson Groups

Let G^tau be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfel'd structure of Poisson group; let H^tau be its dual Poisson group. By means of quantum double construction and dualization via formal Hopf algebras, we construct new quantum groups U_q,phi^M(h) --- dual of U_q,phi^M'(g) --- which yield infinitesimal quantization of H^tau and G^tau; we study their specializations at roots of 1 (in particular, their classical limits), thus discovering new quantum Frobenius morphisms. The whole description dualize for H^tau what was known for G^tau , completing the quantization of the pair (G^tau,H^tau) .