The fake monster algebra and singular Borcherds products
In this paper we consider several problems in the theory of automorphic products and generalized Kac-Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We giv...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
2025
|
| In: |
Advances in mathematics
Year: 2025, Jahrgang: 461, Pages: 1-52 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2024.110083 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aim.2024.110083 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870824005991 
|
| Verfasserangaben: | Haowu Wang, Brandon Williams |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 1925510778 | ||
| 003 | DE-627 | ||
| 005 | 20250717013602.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 250513s2025 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1016/j.aim.2024.110083 |2 doi | |
| 035 | |a (DE-627)1925510778 | ||
| 035 | |a (DE-599)KXP1925510778 | ||
| 035 | |a (OCoLC)1528045305 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Wang, Haowu |d 1993- |e VerfasserIn |0 (DE-588)1365487210 |0 (DE-627)1925511553 |4 aut | |
| 245 | 1 | 4 | |a The fake monster algebra and singular Borcherds products |c Haowu Wang, Brandon Williams |
| 264 | 1 | |c 2025 | |
| 300 | |a 52 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Online verfügbar: 30 December 2024 | ||
| 500 | |a Gesehen am 13.05.2025 | ||
| 520 | |a In this paper we consider several problems in the theory of automorphic products and generalized Kac-Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We give a full classification of symmetric holomorphic Borcherds products of singular weight on lattices of prime level. Finally we prove that all twisted denominator identities of the fake monster algebra arise as the Fourier expansions of Borcherds products of singular weight at a certain cusp. The proofs rely on an identification between modular forms for the Weil representation attached to lattices of type U(N)⊕U⊕L and certain tuples of Jacobi forms of level N. | ||
| 650 | 4 | |a Borcherds products of singular weight | |
| 650 | 4 | |a Conway's group | |
| 650 | 4 | |a Fake monster algebra | |
| 650 | 4 | |a Jacobi forms | |
| 650 | 4 | |a Leech lattice | |
| 650 | 4 | |a Modular forms for the Weil representation | |
| 650 | 4 | |a Twisted denominator identities | |
| 700 | 1 | |a Williams, Brandon |e VerfasserIn |0 (DE-588)1365504948 |0 (DE-627)1925527026 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Advances in mathematics |d Amsterdam [u.a.] : Elsevier, 1961 |g 461(2025), Artikel-ID 110083, Seite 1-52 |h Online-Ressource |w (DE-627)268759200 |w (DE-600)1472893-X |w (DE-576)103373292 |x 1090-2082 |7 nnas |a The fake monster algebra and singular Borcherds products |
| 773 | 1 | 8 | |g volume:461 |g year:2025 |g elocationid:110083 |g pages:1-52 |g extent:52 |a The fake monster algebra and singular Borcherds products |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.aim.2024.110083 |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 856 | 4 | 0 | |u https://www.sciencedirect.com/science/article/pii/S0001870824005991 |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20250513 | ||
| 993 | |a Article | ||
| 994 | |a 2025 | ||
| 998 | |g 1365504948 |a Williams, Brandon |m 1365504948:Williams, Brandon |d 110000 |d 110400 |e 110000PW1365504948 |e 110400PW1365504948 |k 0/110000/ |k 1/110000/110400/ |p 2 |y j | ||
| 999 | |a KXP-PPN1925510778 |e 4724018585 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"title":[{"title_sort":"fake monster algebra and singular Borcherds products","title":"The fake monster algebra and singular Borcherds products"}],"person":[{"given":"Haowu","family":"Wang","role":"aut","display":"Wang, Haowu","roleDisplay":"VerfasserIn"},{"family":"Williams","given":"Brandon","display":"Williams, Brandon","roleDisplay":"VerfasserIn","role":"aut"}],"type":{"media":"Online-Ressource","bibl":"article-journal"},"note":["Online verfügbar: 30 December 2024","Gesehen am 13.05.2025"],"language":["eng"],"recId":"1925510778","origin":[{"dateIssuedDisp":"2025","dateIssuedKey":"2025"}],"id":{"eki":["1925510778"],"doi":["10.1016/j.aim.2024.110083"]},"name":{"displayForm":["Haowu Wang, Brandon Williams"]},"physDesc":[{"extent":"52 S."}],"relHost":[{"origin":[{"publisherPlace":"Amsterdam [u.a.] ; New York, NY [u.a.] ; Orlando, Fla. ; Brugge ; San Diego, Calif. [u.a.]","dateIssuedKey":"1961","publisher":"Elsevier ; Academic Press ; Academic Press ; Academic Press ; Acad. Press","dateIssuedDisp":"1961-"}],"id":{"eki":["268759200"],"zdb":["1472893-X"],"issn":["1090-2082"]},"physDesc":[{"extent":"Online-Ressource"}],"title":[{"title_sort":"Advances in mathematics","title":"Advances in mathematics"}],"pubHistory":["1.1961/65(1965) - 231.2012; Vol. 232.2013 -"],"part":{"text":"461(2025), Artikel-ID 110083, Seite 1-52","volume":"461","extent":"52","year":"2025","pages":"1-52"},"type":{"media":"Online-Ressource","bibl":"periodical"},"disp":"The fake monster algebra and singular Borcherds productsAdvances in mathematics","note":["Gesehen am 14.09.2020"],"recId":"268759200","language":["eng"]}]} | ||
| SRT | |a WANGHAOWUWFAKEMONSTE2025 | ||