Hopf actions of some quantum groups on path algebras

Kinser, Ryan; Oswald, Amrei

doi:10.1016/j.jalgebra.2021.08.002

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“…Recently, combinatorial properties of the Hochschild cohomology of path algebras is studied in terms of the genus of the quiver [23]. Furthermore, the Hopf algebras on path algebras, reconstruction of path algebras and the dimensions of path algebras were studied [3,17,20,21].…”

Section: Introductionmentioning

confidence: 99%

Quivers and path semigroups characterized by locality conditions

Guo¹,

Zheng²

2022

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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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