bibkey: hohnseysen2025monsterautomorphisms authors: Gerald Höhn; Martin Seysen year: 2025 title: The Order of the Monster Finite Simple Group doi: 10.48550/arXiv.2508.01037 url: https://arxiv.org/abs/2508.01037v1 claim: Theorem 2.16 identifies Moonshine VOA automorphisms with invariant-bilinear-form-preserving automorphisms of its degree-two Griess algebra; Theorem 5.7 identifies these full automorphism groups with the Monster. strata_touched: [] license: citation-only triage: anchor

Actual Griess algebra and Moonshine automorphism groups

Primary text: arXiv v1 HTML, v1 PDF.

Section 2.3, Theorem 2.16 states that restriction Aut(V^natural) -> Aut(B), where B=V^natural_2, is an isomorphism. Its next sentence specifies that an automorphism of B also respects its invariant bilinear form. This condition is part of the theorem, not an inference that every algebra has a uniquely recoverable metric.

Section 5, Theorem 5.7 states that the Monster is the full automorphism group of the Griess algebra and the Moonshine module: M=Aut(B)=Aut(V^natural). Its proof uses Theorem 2.16, Carnahan’s order results and Borcherds’ Moonshine theorem. The theorem concerns the actual constructed objects, not a tensor chosen solely by its dimension.

The stable-relation-boundary volume §9 consumes these clauses together with the existing Monster volume §4.1, equations MC.7–MC.11. The latter supplies the positive real form, e=omega/2, g(e,e)=3, W=e^perp, dim W=196883, and the full multiplication reconstruction. The restriction/extension bridge uses exactly the metric-preserving automorphism notion. No coefficients, VOA construction, unrestricted VOA uniqueness, or new Monster identification are supplied by this note.