Cubic rings and the exceptional Jordan algebra
Elkies, Noam D. ; Gross, Benedict H.
Duke Math. J., Tome 110 (2001) no. 1, p. 383-409 / Harvested from Project Euclid
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In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3×3 matrices over the Cayley octonions. Here we use modular forms and Niemeier's classification of even unimodular lattices of rank 24 to further investigate J and the integral, even lattice J0=(ZE)⊥ in J. Specifically, we study ring embeddings of totally real cubic rings A into J which send the identity of A to E, and we give a new proof of R. Borcherds's result that J0 is characterized as a Euclidean lattice by its rank, type, discriminant, and minimal norm.
Publié le : 2001-08-15
Classification:  11H06,  11F27,  11H50,  17C40 
@article{1091737275,
     author = {Elkies, Noam D. and Gross, Benedict H.},
     title = {Cubic rings and the exceptional Jordan algebra},
     journal = {Duke Math. J.},
     volume = {110},
     number = {1},
     year = {2001},
     pages = { 383-409},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1091737275}
}

Elkies, Noam D.; Gross, Benedict H. Cubic rings and the exceptional Jordan algebra. Duke Math. J., Tome 110 (2001) no. 1, pp.  383-409. http://gdmltest.u-ga.fr/item/1091737275/