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

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

1996-04-12

arxiv.org/abs/q-alg/9604009v4

Mathematics

Quantum Algebra

23 pages, AMS-TeX C, Version 3.0; to be published in "Communications in Mathematical Physics". Some misprints are corrected

Scientific paper

10.1007/s002200050054

The present work splits in two parts: first, we perform a straightforward generalization of results from [Re], proving autoquasitriangularity of quantum groups U_q(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 2l-fold ramified covering of the specialization of U_q(g) at a primitive l-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.

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