Brauer图、模operad与电路代数的图式神经定理
Brauer diagrams, modular operads, and a graphical nerve theorem for circuit algebras
AI总结：
本文用Brauer图范畴刻画电路代数，并借助迭代分配律与已有模operad神经定理，证明了电路operad及电路代数的抽象神经定理。
摘要：
用于有限型纽结不变量研究的电路代数，是Jones平面代数的对称类似物。它们与电路operad密切相关，后者是模operad的变体，具备额外的幺半积结构。本文用Brauer图范畴对电路代数进行了刻画。借助迭代分配律及已有的模operad神经定理，证明了适用于电路operad（进而适用于电路代数）的抽象神经定理。
英文摘要：
Circuit algebras, used in the study of finite-type knot invariants, are a symmetric analogue of Jones's planar algebras. They are very closely related to circuit operads, which are a variation of modular operads admitting an extra monoidal product. This paper gives a description of circuit algebras in terms categories of Brauer diagrams. An abstract nerve theorem for circuit operads -- and hence circuit algebras -- is proved using an iterated distributive law, and an existing nerve theorem for modular operads.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
