On the Center of Quantized Enveloping Algebras
On the Center of Quantized Enveloping Algebras
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DOI：
10.1006/jabr.1997.7313
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发表时间：
1998-05
影响因子：
0.9
通讯作者：
Pierre Baumann
中科院分区：
文献类型：
--
作者：
Pierre Baumann
设U是拟三角Hopf代数。可以使用U的R-矩阵来构造节点的标量不变量。类似地，Reshetikhin写下了tangle不变量，这些不变量在U的中心取其值。Reshetikhin的表达式，从而定义中心元素在U。我们在这里证明了一个身份特征的一些这些元素，当U是一个量化的包络代数。作为应用，我们给出了Faddeev，Reshetikhin和Takhtadzhyan关于量子化包络代数中心的一个命题的证明.
Abstract LetUbe a quasitriangular Hopf algebra. One may use theR-matrix ofUin order to construct scalar invariants of knots. Analogously, Reshetikhin wrote down tangle invariants which take their values in the center ofU. Reshetikhin's expressions thus define central elements inU. We prove here an identity characterizing some of these elements, whenUis a quantized enveloping algebra. As an application, we give a proof for a statement of Faddeev, Reshetikhin, and Takhtadzhyan concerning the center of a quantized enveloping algebra.