Mathematics > Quantum Algebra
[Submitted on 13 Mar 2025
]
Title: Structure groupoids of quiver-theoretic Yang-Baxter maps
Title: 图论的Yang-Baxter映射的结构范畴
Abstract: Solutions to the quiver-theoretic quantum Yang-Baxter equation are associated with structure categories and structure groupoids. We prove that the structure groupoids of involutive non-degenerate solutions are Garside. This generalises a well-known result about the structure groups of set-theoretic solutions, due to Chouraqui. We also construct involutive non-degenerate solutions from suitable presented categories. We then investigate the case of solutions of principal homogeneous type. Finally, we present some examples of this new class of Garside groupoids.
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