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arXiv · 2609.07179

A dual theory of Zhu's theory

Hao Wang
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Abstract

We establish a dual theory of Zhu's $A(\mathcal {V})$-theory, i.e., for a graded vertex operator coalgebra $V$, the coassociative coalgebra $C(V)$ are investigated, any admissible $V$-comodule gives a $C(V)$-comodule, and vice versa. We also prove that $V$ is corational, which means every admissible $V$-comodule is completely reducible, if and only if its dual vertex operator algebra $V'$ is rational.

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Hao Wang. 2026-09-07. A dual theory of Zhu's theory. https://arxiv.org/abs/2609.07179

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