On the invertibility of quantization functors
On the invertibility of quantization functors
复制标题
关于量化函子的可逆性
DOI：
10.1016/j.jalgebra.2005.01.056
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发表时间：
2003
影响因子：
0.9
通讯作者：
P. Etingof
中科院分区：
文献类型：
--
作者：
Benjamin Enriquez;P. Etingof
某些量子化问题等价于从“量子”到“经典”道具的态射的构造。一旦这样的态射被构造，亨塞尔引理表明它实际上是一个同构。这给出了一个新的、简单的证明：任何Etingof-Kazhdan量子化函子都是形式级数环上的量子化泛包络（QUE）代数和李双代数（去量子化）之间范畴的等价。我们应用同样的论点来构造量子Yang-Baxter方程和拟三角QUE代数的形式解的去量子化。我们从那里得到一个分类，所有的扭曲杀死一个给定的联想。我们还给出了李双代数的量子化中所涉及的支撑的结构结果，证明了QUE代数的支撑是co-Poisson泛包络代数的支撑的平坦变形.
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.