Expository Automorphic-Correction Description of Lorentzian Kac–Moody Algebras

Definitions and mathematical statement

The supplied record does not specify definitions of a Lorentzian Kac--Moody Lie algebra or superalgebra, a hyperbolic Kac--Moody algebra, or an automorphic correction, including the hypotheses governing these terms. Its original mathematical wording is retained verbatim:

Conjecture: Lorentzian Kac--Moody Lie or superalgebras are automorphic corrections of hyperbolic Kac--Moody algebras.

However, the supplied statement-verification note identifies this sentence in the official report as explanatory background, rather than a conjecture, and marks this record's statement as unrecoverable. Thus the displayed wording is a historical transcription, not a recovered, precisely quantified conjecture. No separate clean mathematical statement is supplied.

The background literature assessment instead discusses the assertion that all Lorentzian Kac--Moody algebras admit automorphic corrections. Being an automorphic correction of a hyperbolic algebra and admitting an automorphic correction are distinct assertions; the record does not reconcile them. Neither assertion is promoted here to a formal conjecture. According to the supplied verification note, the subsequent lattice-specific existence conjecture belongs to the separate record OWR-14605-007; its hypotheses and statement are not supplied here.

Short English statement

This record preserves an expository description relating Lorentzian Kac--Moody Lie algebras and superalgebras to automorphic corrections of hyperbolic Kac--Moody algebras. The supplied verification rejects its original presentation as a separate conjecture. Missing definitions and conflicting existence language prevent a precise independent problem statement.

Sources

• Supplied local registry record: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $30003143$, exact source problem code catalogue entry. No individual proposer is supplied; the proposed year is recorded as $2016$.
• Supplied report citation: Moduli spaces and Modular forms (2017), Oberwolfach Reports, pp. 1259--1318, DOI 10.4171/owr/2016/23. https://doi.org/10.4171/owr/2016/23. The record attributes the material to workshop discussions documented in Oberwolfach Reports.
• Supplied literature reference: Gritsenko--Nikulin, Lorentzian Kac--Moody algebras. https://doi.org/10.1112/plms.12084.
• Supplied literature reference, labelled "early automorphic-correction constructions": https://arxiv.org/abs/alg-geom/9504006.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the record partially_solved and states that automorphic corrections have been constructed in many cases, while a universal conjecture that all Lorentzian Kac--Moody algebras admit such corrections is not proved. This is supplied dated curation, not an independently verified assessment; the record itself requests independent verification of time-sensitive status and cited claims.
• Supplied statement-verification note: the report presents the retained sentence as explanatory background, not a conjecture; the subsequent lattice-specific existence conjecture is assigned to OWR-14605-007. The supplied statement status is unrecoverable, with no clean statement promoted. The record's update timestamp is 2026-09-16T12:06:53Z; it is not identified as a source-verification date.