bibkey: arakawa2016walgebras authors: Tomoyuki Arakawa year: 2016 title: Introduction to W-algebras and their Representation Theory doi: null url: https://arxiv.org/abs/1605.00138v2 claim: The C2 Poisson algebra of a universal affine vertex algebra is the classical coordinate algebra of the dual Lie algebra. strata_touched: [] license: citation-only triage: anchor

Universal affine C2 context

Section 3.8, printed pages 23–24 of arXiv 1605.00138v2, describes the universal affine vertex algebra. Equation (3.19) on printed page 24 identifies its C2 Poisson algebra with the classical coordinate algebra of the dual Lie algebra. 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.

The first arXiv submission is from 2016; the pinned v2 is from 2017. PDF: https://arxiv.org/pdf/1605.00138v2

SHA-256: ed5db1a978c13a824cfaff84ed92d157a982d3fb71871f22461ebf76329c1b4a.

Verified locator

• https://arxiv.org/abs/1605.00138v2: Section 3.8, printed pp. 23–24; (3.19), printed p. 24.
• Classical abstract context only; no actual-$Y$ proof or novelty claim.