论文标题
电路代数是车轮道具
Circuit algebras are wheeled props
论文作者
论文摘要
Bar-Natan和第一作者引入的电路代数是对Jones平面代数的概括，其中人们在“连接图”上删除了平面条件。它们为低维拓扑的虚拟和焊接缠结提供了有用的语言。在本说明中，我们介绍了平面代数众所周知的分类作为具有自偶发器的关键类别的电路代数类似物。我们的主要理论是，电路代数与线性轮毂支柱的类别之间存在类别的等效性 - 一种严格的对称张量类别，具有偶性，在同型理论，变形理论和batalin -Vilkovisky量子形式上。
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams". They provide a useful language for the study of virtual and welded tangles in low-dimensional topology. In this note, we present the circuit algebra analogue of the well-known classification of planar algebras as pivotal categories with a self-dual generator. Our main theorem is that there is an equivalence of categories between circuit algebras and the category of linear wheeled props - a type of strict symmetric tensor category with duals that arises in homotopy theory, deformation theory and the Batalin-Vilkovisky quantization formalism.
