bibkey: bakalovkac2004lattice authors: Bojko Bakalov and Victor G. Kac year: 2004 title: Twisted Modules over Lattice Vertex Algebras doi: 10.1142/9789812702562_0001 url: https://arxiv.org/abs/math/0402315v1 claim: Section 4.1 of arXiv v1 gives the actual lattice generating fields, translation and conformal vector in equations (4.12)-(4.16). strata_touched: [] license: citation-only triage: anchor

Lattice generating fields and conformal data

Section 4.1, printed pages 8–9 of arXiv math/0402315v1, constructs the lattice carrier as the oscillator symmetric algebra tensored with the twisted group algebra of all integral charges. Equations (4.12)–(4.14) give the charged generating field and ordered product. Equation (4.15) specifies translation through its neutral-current commutator and charged ground-state action; (4.16) gives the inverse-form quadratic conformal vector. Theorem 4.1 supplies the surrounding lattice vertex-algebra result. The repository’s actual matrix Sugawara component verifies the mode laws on its existing even-lattice carrier; it does not assert the full all-state vertex-algebra theorem, positivity, or finite-dimensional grading.

The source identification and equation locators are recorded in the existing untwisted lattice input section of the FLM background note. Equation numbers refer to arXiv v1, rather than the published chapter. The rank-one Lean proof architecture adapted for the matrix commutator calculation is separately attributed to Kytölä’s pinned source.

Verified locator

• Primary version: https://arxiv.org/abs/math/0402315v1, §4.1, equations (4.12)–(4.16), Theorem 4.1.
• Published bibliographic identity: https://doi.org/10.1142/9789812702562_0001.