Quantization of Poisson groups -- II

Abstract

Let $G^{\tau }$ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfeld structure of Poisson group; let $H^{\tau }$ be its dual Poisson group. By means of Drinfeld's double construction and dualization via formal Hopf algebras, we construct new quantum groups $U_{q,\varphi }^M(\mathfrak{h})$ --- dual of $U_{q,\varphi }^{M^{\prime }}(\mathfrak{g})$ --- 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 $(G^{\tau },H^{\tau })$.

This preprint was withdrawn because its content is included in the (now updated) preprint arXiv:q-alg/9511022