bibkey: li2004abelianizing authors: Haisheng Li year: 2004 title: Abelianizing vertex algebras doi: null url: https://arxiv.org/abs/math/0409140v1 claim: Zhu’s C2 quotient has multiplication induced by mode -1 and Poisson bracket induced by mode 0. strata_touched: [] license: citation-only triage: anchor

C2 filtration and Poisson quotient context

Printed page 15 of arXiv math/0409140v1 (2004), Corollary 3.6, gives $E_1(W)=C_2(W)$ for a vertex-algebra module $W$. Proposition 3.7 recalls Zhu’s Poisson algebra $V/C_2(V)$; equation (3.15) gives its multiplication by mode $-1$ and bracket by mode $0$. This is classical abstract context; it does not itself prove the specified concrete bridge from the actual polynomial Fock state field $Y$ to $C_2(F)=\ker \pi$ and its nonpositive-mode formulas.

PDF: https://arxiv.org/pdf/math/0409140v1

SHA-256: b6d59b8158c3753af30bf3e23c3702aeddbb05318ebb4895b2c0ca693351e6ad.

Verified locator

• https://arxiv.org/abs/math/0409140v1: printed p. 15, Corollary 3.6, Proposition 3.7 and (3.15).
• Classical abstract context only; no actual-$Y$ proof or novelty claim.