Quantization of Poisson groups

Fabio Gavarini

Vol. 186 (1998), No. 2, 217–266

DOI: 10.2140/pjm.1998.186.217

Abstract

Let G^τ be a connected simply connected semisimple algebraic group, endowed with generalized Sklyanin-Drinfel’d structure of Poisson group; let H^τ be its dual Poisson group. By means of quantum double construction and dualization via formal Hopf algebras, we construct new quantum groups U_q,φ^M(h) — dual of U _q,φ^M′(g) — which yield infinitesimal quantization of H^τ and G^τ ; 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^τ what was known for G^τ, completing the quantization of the pair (G^τ,H^τ).

Milestones

Received: 10 February 1997

Revised: 1 April 1997

Published: 1 December 1998