Geometrical Meaning of R-matrix Action for Quantum Groups at Roots of 1

Abstract

The present work splits in two parts: first, we perform a straightforward generalization of results from [Re], proving autoquasitriangularity of quantum groups $U_q(\mathfrak{g})$ and their unrestricted specializations at roots of 1, in particular the function algebra $F[H]$ of the Poisson group $H$ dual of $G$; second, as a main contribution, we prove the convergence of the (specialized) $R$--matrix action to a birational automorphism of a 2$\ell$--fold ramified covering of the specialization of $U_q(\mathfrak{g})$ at a primitive $\ell$--th root of 1, and of a 2-fold ramified covering of $H$, thus giving a geometric content to the notion of triangularity (or autoquasitriangularity) for quantum groups.

23 pages, AMS-TeX C, Version 3.0; final author's version, as appeared in the printed paper

References in corpus (1)

• Quasitriangularity of quantum groups at roots of 1

Cited by in corpus (6)

• Invariants of links with flat connections in their complements.II. Holonomy R-matrices related to quantized universal enveloping algebras at roots of 1
• Tressages des groupe de Poisson formels à dual quasitriangulaire
• The $R$--matrix action of untwisted affine quantum groups at roots of 1
• Tensor K-matrices for quantum symmetric pairs
• Braiding structures on formal Poisson groups and classical solutions of the QYBE
• Braidings of Poisson groups with quasitriangular dual (Tressages des groupes de Poisson à dual quasitriangulaire)