bibkey: flm1988monster authors: Igor B. Frenkel, James Lepowsky, and Arne Meurman year: 1988 title: Vertex Operator Algebras and the Monster doi: 10.1016/S0079-8169(08)X6136-7 claim: Construction and theory of the Monster vertex operator algebra; not a proof of this repository’s determinant interface. strata_touched: [] license: citation-only triage: anchor

Monster vertex operator algebra

Frenkel, Lepowsky, and Meurman construct the Monster module used in monstrous moonshine. Borcherds’s 1992 introduction explicitly identifies their graded Monster representation as the input to his proof. This book does not by itself identify a formal determinant with the bivariate denominator in the repository’s Lean carrier.

A chiral VOA construction does not by itself supply a full CFT, a string model, or a holographic dual. The separate holographic scopes are described in the Maldacena note and the JLMS note.

Verified locator

• Book title, year, and DOI: https://doi.org/10.1016/S0079-8169(08)X6136-7
• Borcherds 1992, introduction, names the FLM representation: https://math.berkeley.edu/~reb/papers/monster/monster.tex

The bibliographic identity and Borcherds’s attribution were checked; the FLM book’s full text was not inspected.

Untwisted lattice input (Bakalov–Kac)

The untwisted lattice input used before the reflection-twisted Monster extension is the construction in BK2004v1: Bojko Bakalov and Victor G. Kac, Twisted Modules over Lattice Vertex Algebras, §4.1. The cited section is on printed pp. 8–9 of arXiv v1 (2004-02-19). For an integral lattice $Q$, that section forms $V_Q=S\otimes {\mathbb{C}}_{\epsilon }[Q]$, with the twisted group-algebra multiplication and charge shift in (4.3) and (4.6), then defines the exponential generating field in (4.12) and the ordered two-field product in (4.14) used for locality. Theorem 4.1 states the resulting lattice vertex-algebra structure. The paper allows odd integral lattices with parity; for an even lattice that parity is zero, which is the prospective ordinary lattice scope here.

This source supports the untwisted lattice construction used before the reflection-twisted Monster extension; it is not itself a complete Monster, full-CFT, string, or AdS/CFT result. The existing PolynomialFockChargedStateField.chargedY stays on a fixed polynomial Fock carrier and is not the displayed charge-changing direct-sum field. BK2004v1 is the inspected arXiv v1 source; Crossref independently matches its authors and title to the chapter in Lie Theory and Its Applications in Physics V (2004), pp. 3–26, DOI 10.1142/9789812702562_0001. The equation and theorem numbers below refer to arXiv v1, not to an inspected published chapter. These literature references do not establish a Lean realization of the charge-changing lattice fields.

• §4.1, (4.3) and (4.6): $e_{\alpha }{e}_{\beta }=\epsilon (\alpha ,\beta )e_{\alpha +\beta }$ and $e_{\gamma }(s\otimes e_{\alpha })=\epsilon (\gamma ,\alpha )s\otimes e_{\alpha +\gamma }$, respectively.
• §4.1, (4.12) and (4.14): the exponential field $Y_{\alpha }(z)$ and the ordered product $Y_{\alpha }(z)Y_{\beta }(w)$ underlying mutual locality.
• §4.1, Theorem 4.1: the fields $h(z)$ and $Y_{\alpha }(z)$ generate the vertex-algebra structure on $V_Q$, with the displayed translation and conformal data in (4.15)–(4.16).