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arXiv · 2606.14407

Zhu's algebra and the $C_2$-algebra of a classically free vertex operator algebra

Bailin Song·Xianlong Zeng
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Abstract

We prove that, for a classically free vertex algebra, the $C_2$-algebra is naturally isomorphic to the associated graded algebra of Zhu's algebra. As an application, we show that non-trivial holomorphic VOAs of CFT type are not classically free. This includes the affine vertex operator algebra of $E_8$ at level one, as well as the Moonshine VOA.

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Bailin Song, Xianlong Zeng. 2026-06-12. Zhu's algebra and the $C_2$-algebra of a classically free vertex operator algebra. https://arxiv.org/abs/2606.14407

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