Le centre des algèbres de coordonnées des groupes quantiques aux racines -ièmes de l’unité
Quantization of canonical cones of algebraic curves
We introduce a quantization of the graded algebra of functions on the canonical cone of an algebraic curve , based on the theory of formal pseudodifferential operators. When is a complex curve with Poincaré uniformization, we propose another, equivalent construction, based on the work of Cohen-Manin-Zagier on Rankin-Cohen brackets. We give a presentation of the quantum algebra when is a rational curve, and discuss the problem of constructing algebraically “differential liftings”.
PBW and duality theorems for quantum groups and quantum current algebras.
A formula for the logarithm of the KZ associator.
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