Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493428 | Journal of Algebra | 2005 | 25 Pages |
Abstract
Certain quantization problems are equivalent to the construction of morphisms from “quantum” to “classical” props. Once such a morphism is constructed, Hensel's lemma shows that it is in fact an isomorphism. This gives a new, simple proof that any Etingof-Kazhdan quantization functor is an equivalence of categories between quantized universal enveloping (QUE) algebras and Lie bialgebras over a formal series ring (dequantization). We apply the same argument to construct dequantizations of formal solutions of the quantum Yang-Baxter equation and of quasitriangular QUE algebras. We derive from there a classification of all twistors killing a given associator. We also give structure results for the props involved in quantization of Lie bialgebras, which yield an associator-independent proof that the prop of QUE algebras is a flat deformation of the prop of co-Poisson universal enveloping algebras.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Benjamin Enriquez, Pavel Etingof,