Quantization of Poisson groups -- II

Details Quantization of Poisson groups -- II Quantization of Poisson groups -- II

1996-04-10

arxiv.org/abs/q-alg/9604007v3

Mathematics

Quantum Algebra

58 pages, AMS-TeX C, Version 3.0. Some important formulas 1.4, 5.16, and 6.9 have been corrected; the constructions and result

Scientific paper

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,\phi}^M ({\frak h}) $ --- dual of $ U_{q,\phi}^{M'} ({\frak 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) $.

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