Critical CoHAs, vertex coalgebras and Deformed Drinfeld coproducts
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915883069210624 |
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| author | Jindal, Shivang Kaubrys, Sarunas Latyntsev, Alexei |
| author_facet | Jindal, Shivang Kaubrys, Sarunas Latyntsev, Alexei |
| contents | We construct a vertex coproduct on the Kontsevich--Soibelman cohomological Hall algebra (CoHA) of a quiver with potential, following Joyce (2018). We show it forms a vertex bialgebra. By applying a vertex algebraic analogue of Majid--Radford bosonisation, we form an extension of the CoHA of quivers with potential which incorporates a Cartan part. In the case of ADE quivers our vertex coproduct recovers Drinfeld's deformed coproduct on the Yangian. We compare the vertex coproduct with a localised coproduct defined by Davison and with the construction of Dotsenko--Mozgovoy when the potential is trivial. Our construction gives a new proof of the cohomological integrality theorem for symmetric quivers with trivial potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21707 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Critical CoHAs, vertex coalgebras and Deformed Drinfeld coproducts Jindal, Shivang Kaubrys, Sarunas Latyntsev, Alexei Representation Theory Algebraic Geometry Quantum Algebra We construct a vertex coproduct on the Kontsevich--Soibelman cohomological Hall algebra (CoHA) of a quiver with potential, following Joyce (2018). We show it forms a vertex bialgebra. By applying a vertex algebraic analogue of Majid--Radford bosonisation, we form an extension of the CoHA of quivers with potential which incorporates a Cartan part. In the case of ADE quivers our vertex coproduct recovers Drinfeld's deformed coproduct on the Yangian. We compare the vertex coproduct with a localised coproduct defined by Davison and with the construction of Dotsenko--Mozgovoy when the potential is trivial. Our construction gives a new proof of the cohomological integrality theorem for symmetric quivers with trivial potential. |
| title | Critical CoHAs, vertex coalgebras and Deformed Drinfeld coproducts |
| topic | Representation Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2603.21707 |