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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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Cite

BibTeXRIS
BibTeX
@misc{minets2026quantum,
  title = {{Quantum wreath products and Yang-Baxter equations}},
  author = {Alexandre Minets},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02765},
  eprint = {2609.02765},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02765},
}
RIS
TY  - UNPB
TI  - Quantum wreath products and Yang-Baxter equations
AU  - Alexandre Minets
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2609.02765
UR  - https://arxiv.org/abs/2609.02765
AB  - 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.
ER  -