Geodesic
A Composite Order Generalization of Modular Moonshine
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce a generalization of Brauer character to allow arbitrary finite length modules over discrete valuation rings. We show that the generalized super Brauer character of Tate cohomology is a linear combination of trace functions. Using this result, we find a counterexample to a conjecture of Borcherds about vanishing of Tate cohomology for Fricke elements of the Monster.
Keywords: moonshine, modular function, Brauer character, vertex operator algebra. 
@article{SIGMA_2021_17_a109,
     author = {Satoru Urano},
     title = {A {Composite} {Order} {Generalization} of {Modular} {Moonshine}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
     volume = {17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a109/}
}
TY  - JOUR
AU  - Satoru Urano
TI  - A Composite Order Generalization of Modular Moonshine
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2021
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a109/
LA  - en
ID  - SIGMA_2021_17_a109
ER  - 
%0 Journal Article
%A Satoru Urano
%T A Composite Order Generalization of Modular Moonshine
%J Symmetry, integrability and geometry: methods and applications
%D 2021
%V 17
%U http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a109/
%G en
%F SIGMA_2021_17_a109
Satoru Urano. A Composite Order Generalization of Modular Moonshine. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a109/

[1] Borcherds R. E., “Monstrous moonshine and monstrous Lie superalgebras”, Invent. Math., 109 (1992), 405–444 | DOI | MR | Zbl

[2] Borcherds R. E., “Modular moonshine. III”, Duke Math. J., 93 (1998), 129–154, arXiv: math.AG/9801101 | DOI | MR | Zbl

[3] Borcherds R. E., Ryba A. J. E., “Modular Moonshine. II”, Duke Math. J., 83 (1996), 435–459 | DOI | MR | Zbl

[4] Carnahan S., “A self-dual integral form of the Moonshine module”, SIGMA, 15 (2019), 030, 36 pp., arXiv: 1710.00737 | DOI | MR | Zbl

[5] Cassels J. W. S., Fröhlich A. (eds.), Algebraic number theory, Academic Press, London, Thompson Book Co., Inc., Washington, D.C., 1967 | MR | Zbl

[6] Conway J. H., Norton S. P., “Monstrous moonshine”, Bull. London Math. Soc., 11 (1979), 308–339 | DOI | MR | Zbl

[7] Frenkel I., Lepowsky J., Meurman A., Vertex operator algebras and the Monster, Pure and Applied Mathematics, 134, Academic Press, Inc., Boston, MA, 1988 | MR | Zbl