Equivariant vertex coalgebras, $C_2$-coalgebras and duality for diagonalisable group schemes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910773635186688 |
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| author | Caradot, Antoine Lin, Zongzhu |
| author_facet | Caradot, Antoine Lin, Zongzhu |
| contents | In this paper, we define vertex algebras and vertex coalgebras in the category of rational $G_Γ$-modules, where $G_Γ$ is the group scheme defined by the group algebra $\mathsf k Γ$ for an abelian group $Γ$. In this context, we introduce the notion of $C_2$-coalgebra for a vertex coalgebra. We prove that there exists a duality between vertex algebras and vertex coalgebras in the category of $G_Γ$-modules, and this duality establishes a connection between $C_2$-algebras and $C_2$-coalgebras. Moreover, we also investigate the relationship between their respective modules/comodules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02661 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant vertex coalgebras, $C_2$-coalgebras and duality for diagonalisable group schemes Caradot, Antoine Lin, Zongzhu Representation Theory Quantum Algebra In this paper, we define vertex algebras and vertex coalgebras in the category of rational $G_Γ$-modules, where $G_Γ$ is the group scheme defined by the group algebra $\mathsf k Γ$ for an abelian group $Γ$. In this context, we introduce the notion of $C_2$-coalgebra for a vertex coalgebra. We prove that there exists a duality between vertex algebras and vertex coalgebras in the category of $G_Γ$-modules, and this duality establishes a connection between $C_2$-algebras and $C_2$-coalgebras. Moreover, we also investigate the relationship between their respective modules/comodules. |
| title | Equivariant vertex coalgebras, $C_2$-coalgebras and duality for diagonalisable group schemes |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2501.02661 |