Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$

[1905.09629] Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$ Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:1905.09629 (math) [Submitted on 23 May 2019 ( v1 ), last revised 3 Feb 2021 (this version, v2)] Title: Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$ Authors: Sven Möller View a PDF of the paper titled Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$, by Sven M\"oller View PDF HTML (experimental) Abstract: Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of square-free level. These belong to a larger class of Borcherds-Kac-Moody (super)algebras Borcherds obtained by twisting the denominator identity of the Fake Monster Lie algebra. Borcherds asked whether these Lie (super)algebras admit natural constructions. For the ten Lie algebras from the classification we give a positive answer to this question, i.e. we prove that they can be realised uniformly as the BRST cohomology of suitable vertex algebras. Comments: 34 pages, LaTeX; minor revisions, some proofs expanded, numbering changed; to appear in Comm. Math. Phys Subjects: Quantum Algebra (math.QA) ; Representation Theory (math.RT) MSC classes: 17B69, 17B65, 17B67 Cite as: arXiv:1905.09629 [math.QA] (or arXiv:1905.09629v2 [math.QA] for this version) https://doi.org/10.48550/arXiv.1905.09629 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Comm. Math. Phys., 383(1):35-70, 2021 Related DOI : https://doi.org/10.1007/s00220-021-04018-w Focus to learn more DOI(s) linking to related resources Submission history From: Sven Möller [ view email ] [v1] Thu, 23 May 2019 13:01:31 UTC (35 KB) [v2] Wed, 3 Feb 2021 11:49:15 UTC (41 KB) Full-text links: Access Paper: View a PDF of the paper titled Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$, by Sven M\"oller View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2019-05 Change to browse by: math math.RT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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