论文标题
部分可观测时空混沌系统的无模型预测
Invertible bimodule categories and generalized Schur orthogonality
论文作者
论文摘要
Schur正交关系是群体代表理论中的基石。我们利用对弱的HOPF代数的概括来在骨骼数据上提供新的，易于验证的条件，以确定给定的双模模类别是否可逆，因此定义了莫里塔等效性。作为第一个应用程序，我们提供了一种算法，用于构建与给定模块类别相关的可逆双模块类别的完整骨骼数据，当基础类别是单位时，该算法是在单一尺度上获得的。作为第二个应用程序，我们表明我们的可逆性条件等同于MPO注射率的概念，从而结束了一个关于拓扑序列的字符串网络模型的张量网络表示的开放问题。我们讨论了广义对称性的应用，包括广义的wigner-eckart定理。
The Schur orthogonality relations are a cornerstone in the representation theory of groups. We utilize a generalization to weak Hopf algebras to provide a new, readily verifiable condition on the skeletal data for deciding whether a given bimodule category is invertible and therefore defines a Morita equivalence. As a first application, we provide an algorithm for the construction of the full skeletal data of the invertible bimodule category associated to a given module category, which is obtained in a unitary gauge when the underlying categories are unitary. As a second application, we show that our condition for invertibility is equivalent to the notion of MPO-injectivity, thereby closing an open question concerning tensor network representations of string-net models exhibiting topological order. We discuss applications to generalized symmetries, including a generalized Wigner-Eckart theorem.
