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arXiv · 2207.11058

Quivers and path semigroups characterized by locality conditions

Li Guo·Shanghua Zheng
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Abstract

The notion of locality semigroups was recently introduced 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 given by the paths of quivers. Further these path semigroups from paths are precisely the free objects in the category of locality semigroups with a rigid condition. This characterization gives a universal property of path algebras and at the same time a combinatorial realization of free rigid locality semigroups.

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Li Guo, Shanghua Zheng. 2022-07-22. Quivers and path semigroups characterized by locality conditions. https://arxiv.org/abs/2207.11058

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