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15 Ausust 2001 Cubic rings and the exceptional Jordan algebra
Noam D. Elkies, Benedict H. Gross
Duke Math. J. 109(2): 383-409 (15 Ausust 2001). DOI: 10.1215/S0012-7094-01-10924-1

Abstract

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.

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Noam D. Elkies. Benedict H. Gross. "Cubic rings and the exceptional Jordan algebra." Duke Math. J. 109 (2) 383 - 409, 15 Ausust 2001. https://doi.org/10.1215/S0012-7094-01-10924-1

Information

Published: 15 Ausust 2001
First available in Project Euclid: 5 August 2004

zbMATH: 1028.11041
MathSciNet: MR1845183
Digital Object Identifier: 10.1215/S0012-7094-01-10924-1

Subjects:
Primary: 11H06
Secondary: 11F27 , 11H50 , 17C40

Rights: Copyright © 2001 Duke University Press

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Vol.109 • No. 2 • 15 Ausust 2001
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