A Construction Method for Albert Algebras over Algebraic Varieties

Abstract

We construct cubic Jordan algebras over an integral proper scheme X such that 2, 3 ∈ H ⁰(X, 𝒪 _X ), generalizing a construction by B. N. Allison and J. R. Faulkner. In the process, we obtain admissible cubic algebras and pseudocomposition algebras over X. Results on the structure of these algebras are obtained, as well as examples over elliptic curves.

Key Words:

• Admissible cubic algebras
• Albert algebras
• Elliptic curve
• Jordan algebras
• Pseudo-composition algebras

2010 Mathematics Subject Classification:

• Primary 17C50
• Secondary 17C40, 17A30

Notes

Communicated by I. Shestakov.