Monoidal categorification from alternating snakes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917226964058112 |
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| author | Brito, Matheus Chari, Vyjayanthi |
| author_facet | Brito, Matheus Chari, Vyjayanthi |
| contents | In a recent paper, the authors introduced the notion of an alternating snake and a corresponding family of finite dimensional modules for the quantum affine algebra associated to $A_n$. We prove that under some restrictions, an alternating snake defines a canonical monoidal category. We prove that this category has finitely many prime objects. As a consequence we prove that the Grothendieck ring is isomorphic to the Grothendieck ring of the category $\mathscr C_ξ$ for a suitable height function. In particular it follows that the special family of alternating snakes provides a monoidal categorification of a cluster algebra of type $A_N$ for a suitable value of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20111 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monoidal categorification from alternating snakes Brito, Matheus Chari, Vyjayanthi Quantum Algebra Representation Theory In a recent paper, the authors introduced the notion of an alternating snake and a corresponding family of finite dimensional modules for the quantum affine algebra associated to $A_n$. We prove that under some restrictions, an alternating snake defines a canonical monoidal category. We prove that this category has finitely many prime objects. As a consequence we prove that the Grothendieck ring is isomorphic to the Grothendieck ring of the category $\mathscr C_ξ$ for a suitable height function. In particular it follows that the special family of alternating snakes provides a monoidal categorification of a cluster algebra of type $A_N$ for a suitable value of $N$. |
| title | Monoidal categorification from alternating snakes |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2601.20111 |