Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices

[2010.00849] Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:2010.00849 (math) [Submitted on 2 Oct 2020 ( v1 ), last revised 2 Feb 2026 (this version, v3)] Title: Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices Authors: Gerald Höhn , Sven Möller View a PDF of the paper titled Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices, by Gerald H\"ohn and 1 other authors View PDF HTML (experimental) Abstract: We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ of central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold constructions associated with the 24 Niemeier lattice vertex operator algebras $V_N$ and certain 226 short automorphisms in $\operatorname{Aut}(V_N)$. We show that up to algebraic conjugacy these automorphisms are exactly the generalised deep holes, as introduced in arXiv:1910.04947 , of the Niemeier lattice vertex operator algebras with the additional property that their orders are equal to those of the corresponding outer automorphisms. Together with the constructions in arXiv:1708.05990 and arXiv:1910.04947 this gives three different uniform constructions of these vertex operator algebras, which are related through 11 algebraic conjugacy classes in $\operatorname{Co}_0$. Finally, by considering the inverse orbifold constructions associated with the 226 short automorphisms, we give the first systematic proof of the result that each strongly rational, holomorphic vertex operator algebra $V$ of central charge 24 with non-zero weight-one space $V_1$ is uniquely determined by the Lie algebra structure of $V_1$. Comments: 42 pages, LaTeX; added a missing assumption in Proposition 2.2 and fixed a typo in Table 1 Subjects: Quantum Algebra (math.QA) ; Representation Theory (math.RT) MSC classes: 17B69 Cite as: arXiv:2010.00849 [math.QA] (or arXiv:2010.00849v3 [math.QA] for this version) https://doi.org/10.48550/arXiv.2010.00849 Focus to learn more arXiv-issued DOI via DataCite Journal reference: J. Lond. Math. Soc., 106(4):3162-3207, 2022 Related DOI : https://doi.org/10.1112/jlms.12659 Focus to learn more DOI(s) linking to related resources Submission history From: Sven Möller [ view email ] [v1] Fri, 2 Oct 2020 08:28:33 UTC (43 KB) [v2] Tue, 2 Aug 2022 07:49:36 UTC (45 KB) [v3] Mon, 2 Feb 2026 17:45:50 UTC (45 KB) Full-text links: Access Paper: View a PDF of the paper titled Systematic Orbifold Constructions of Schellekens' Vertex Operator Algebras from Niemeier Lattices, by Gerald H\"ohn and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2020-10 Change to browse by: math math.RT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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