On the invertibility of quantization functors
摘要
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 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.
引用
@article{arxiv.math/0306212,
title = {On the invertibility of quantization functors},
author = {B. Enriquez and P. Etingof},
journal= {arXiv preprint arXiv:math/0306212},
year = {2007}
}