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Quantization of braided derivations for algebras with grading or action

Le : 08/11/2006 14h15
Par : Hilja L. Huru (Institute of Mathematics and Statistics, University of TromsØ, N-9037 TromsØ, Norway)
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Résumé : We consider quantizations and braidings of modules with grading or action by a finite abelian group. We find an explicit description of quantization and braidings for the graded case. Using the Fourier transform find the corresponding description when the action is by the dual group. We will look at quantization of braided derivations in algebras, braided connections and curvatures. One example is sl2 (C). By considering derivations of the exterior algebra of the semisimple algebra, hence extending the grading by Z, we get quantizations alternative to quantum groups. Another example is grading by Zn, action by its dual the n-dimensional torus, Tn, and the algebra of polynomials in n variables. This can be applied to integrable mechanical systems.