Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
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Sklyanin 行列式、拉普拉斯算子和经典李代数的特征恒等式
DOI：
10.1063/1.531366
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发表时间：
1995
影响因子：
1.3
通讯作者：
A. Molev
中科院分区：
文献类型：
--
作者：
A. Molev
研究了称为扭曲杨吉安的量化包络代数的结构，它与经典李代数的B、C和D系列自然联系在一起。得到了扭杨数中心的自由生成元的形式级数（Sklyanin行列式）的一个显式公式。作为推论，得到了正交和辛李代数的泛包络代数的中心的代数独立生成元的新系统，并找到了由这些李代数的生成元构成的矩阵的特征多项式.
The structure of quantized enveloping algebras called twisted Yangians, which are naturally associated with the B, C, and D series of the classical Lie algebras is studied. An explicit formula for the formal series (the Sklyanin determinant), whose coefficients are free generators of the center of the twisted Yangian is obtained. As a corollary a new system of algebraically independent generators of the center of the universal enveloping algebra for the orthogonal and symplectic Lie algebras is obtained and the characteristic polynomial for the matrix formed by the generators of these Lie algebras is found.