论文标题
量子矢量字段通过量子加倍及其应用
Quantum vector fields via quantum doubles and their applications
论文作者
论文摘要
通过将对应于Hecke对称的反射方程代数的发生器作为矢量场的量子类似物，我们通过所谓的量子双打展示了相应的Leibniz规则。函数代数在这种双重双重方向中的作用归因于反射方程代数的另一副本。我们考虑两种类型的量子双打：这些产生作用于函数代数的左量矢量场的量子类似物以及引起作用于同一代数的伴随矢量场的量子类似物的量子类似物。此外，我们在反射方程代数的发电机中引入量子部分衍生物，然后在限制$ q \ rightarrow 1 $中引入量子衍生物1 $，我们在包裹的代数$ u（gl_n）$以及在某些扩展方面获得了量子部分衍生物。
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra in such a double is attributed to another copy of the reflection equation algebra. We consider two types of quantum doubles: these giving rise to the quantum analogs of left vector fields acting on the function algebra and those giving rise to quantum analogs of the adjoint vector fields acting on the same algebra. Also, we introduce quantum partial derivatives in the generators of the reflection equation algebra and then at the limit $q\rightarrow 1$ we get quantum partial derivatives on the enveloping algebra $U(gl_N)$ as well as on a certain its extension.
