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arXiv · 2501.02661

Equivariant vertex coalgebras, $C_2$-coalgebras and duality for diagonalisable group schemes

Antoine Caradot·Zongzhu Lin
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Abstract

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.

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BibTeXRIS

Antoine Caradot, Zongzhu Lin. 2025-01-05. Equivariant vertex coalgebras, $C_2$-coalgebras and duality for diagonalisable group schemes. https://arxiv.org/abs/2501.02661

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