Quivers and path semigroups characterized by locality conditions
Quivers and path semigroups characterized by locality conditions
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DOI：
10.1007/s10801-023-01281-z
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发表时间：
2022-07
影响因子：
0.8
通讯作者：
Shanghua Zheng;Li Guo
中科院分区：
文献类型：
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作者：
Shanghua Zheng;Li Guo
箭图上的路代数是代数的一个基本类，有着广泛的应用。然而，它是具有挑战性的描述其普遍性质，因为其基础的道路半群只是部分定义。局部性结构是近年来提出的一个新概念，用来处理部分定义的操作，其理论基础是凸几何和量子场论中的局部性。我们发现，有一个自然的对应关系之间的局部集和箭图，导致一个具体的类的局部半群，称为布兰特局部半群，它可以得到的路径箭图。进一步地，这些路Brandt局部性半群正是具有刚性条件的Brandt局部性半群范畴中的自由对象。这个刻画给出了路代数的一个普适性质，同时也给出了自由刚性Brandt局部半群的一个组合实现。
Path algebras from quivers are a fundamental class of algebras with wide applications. Yet it is challenging to describe their universal properties since their underlying path semigroups are only partially defined. A new notion, called locality structures, was recently introduced to deal with partially defined operation, with motivation from locality in convex geometry and quantum field theory. We show that there is a natural correspondence between locality sets and quivers which leads to a concrete class of locality semigroups, called Brandt locality semigroups, which can be obtained by the paths of quivers. Further these path Brandt locality semigroups are precisely the free objects in the category of Brandt locality semigroups with a rigidity condition. This characterization gives a universal property of path algebras and at the same time a combinatorial realization of free rigid Brandt locality semigroups.