Jordan Algebras Over Algebraic Varieties

Abstract

General results on the module structure of Jordan algebras over locally ringed spaces are obtained. Albert algebras over a Brauer–Severi variety with associated central simple algebra of degree 3 are constructed using generalizations of the Tits process and the first Tits construction.

Key Words:

• Albert algebras
• Brauer–Severi variety
• First Tits construction
• Jordan algebras
• Tits process

2000 Mathematics Subject Classification:

• Primary: 17C40

ACKNOWLEDGMENTS

The author would like to acknowledge the support of the “Georg-Thieme-Gedächtnisstiftung” (Deutsche Forschungsgemeinschaft) during her stay at the University of Trento in 2005–06, where most of this paper was written, and thanks the Department of Mathematics at the University of Trento for its hospitality.

Notes

Communicated by I. Shestakov