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arXiv · 2609.02765

Quantum wreath products and Yang-Baxter equations

Alexandre Minets
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Abstract

We extend the setup of Lai-Nakano-Xiang's quantum wreath product algebras to symmetric monoidal categories and deformed braid relations. Under some mild assumptions, we drastically simplify the criterion for such algebras to have PBW basis; curiously, the new criterion is phrased in terms of associative and quantum Yang-Baxter equations. As an application, we clean up some basis results in the existing literature, and propose a certain generalization of quiver Hecke algebras.

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Alexandre Minets. 2026-09-02. Quantum wreath products and Yang-Baxter equations. https://arxiv.org/abs/2609.02765

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