论文标题
部分可观测时空混沌系统的无模型预测
Diagram categories and invariant theory for classical groups and supergroups
论文作者
论文摘要
我们介绍了一个图类别的概念，并讨论了其在古典组和超级群体的不变理论中的应用，其中有一些指示，涉及量子组和量子超级群体的扩展。引入了从各个图类别到表示类别的张量函数，并研究了其属性，从而导致经典超级群体不变理论的第一和第二基本定理，其中包括经典群体作为特殊情况。示意方法的应用使构造正交和符号群的内态代数的介绍，从而导致了由Brauer和Weyl的工作提出的解决方案的解决方案。
We introduce the notion of a diagram category and discuss its application to the invariant theory of classical groups and super groups, with some indications concerning extensions to quantum groups and quantum super groups. Tensor functors from various diagram categories to categories of representnations are introduced and their properties investigated, leading to first and second fundamental theorems of invariant theory for classical super groups, which include the classical groups as special cases. Application of diagrammatic methods enables the constructionof a presentation for endomorphism algebras for te orthogonal and symplectic groups, leading to the solution ofproblems raised by the work of Brauer and Weyl.
