论文标题
Superalgebra $ gl（1 | 1）$的Drinfeld-Kohno定理
The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$
论文作者
论文摘要
在通用AFFNE级别和表示参数的情况下，我们重新审查了Knizhnik-Zamolodchikov方程的推导。 Superalgebra $ gl（1 | 1）$的渐近解决方案的存在及其属性证明为存在的存在协会证明，该证明满足了编织的张量类别的要求。 $ u_h（gl（1 | 1））$量子代数的编织张量类别结构计算出，并且张量产品环被证明是对$ gl（1 | 1）$环的同构，对于模块的级别和参数之间的相同的通用关系。我们回顾了Geer建议的非隔离性模块类别的Drinfeld-Kohno定理的证明，并表明它对于Superalgebra $ gl（1 | 1）$仍然有效。还提供了KZ方程的对数解的示例。
We revisit the derivation of Knizhnik-Zamolodchikov equations in the case of nonsemisimple categories of modules of a superalgebra in the case of the generic affne level and representations parameters. A proof of existence of asymptotic solutions and their properties for the superalgebra $gl(1|1)$ gives a basis for the proof of existence associator which satisfy braided tensor categories requirements. Braided tensor category structure of $U_h(gl(1|1))$ quantum algebra calculated, and the tensor product ring is shown to be isomorphic to $gl(1|1)$ ring, for the same generic relations between the level and parameters of modules. We review the proof of Drinfeld-Kohno theorem for non-semisimple category of modules suggested by Geer and show that it remains valid for the superalgebra $gl(1|1)$. Examples of logarithmic solutions of KZ equations are also presented.
