论文标题
Y产品
The Y-Product
论文作者
论文摘要
我们提出了一种拓扑结构，提供了许多非交流性frobenius代数的例子，这些代数概括了众所周知的裤子。当应用于固体圆环时，与起重机理论结合使用时，我们提供了Verlinde公式的拓扑证明。我们还将构造应用于较高属的固体手柄，从而导致verlinde公式的概括（不是较高的Verlinde属公式）。特别是，我们定义了广义的$ s $ -matrix。最后，我们讨论了我们的构建与Yetter作为Hopf代数的构造之间的关系，并进行概括。
We present a topological construction that provides many examples of non-commutative Frobenius algebras that generalizes the well-known pair-of-pants. When applied to the solid torus, in conjunction with Crane-Yetter theory, we provide a topological proof of the Verlinde formula. We also apply the construction to a solid handlebody of higher genus, leading to a generalization of the Verlinde formula (not the higher genus Verlinde formula); in particular, we define a generalized $S$-matrix. Finally, we discuss the relation between our construction and Yetter's construction of a handle as a Hopf algebra, and give a generalization.
