Albert algebras over Z and other rings

Abstract

Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative non-associative algebras and also arise naturally in the context of simple affine group schemes of type $F_4$, $E_6$, or $E_7$. We study these objects over an arbitrary base ring $R$, with particular attention to the case of the integers. We prove in this generality results previously in the literature in the special case where $R$ is a field of characteristic different from 2 and 3.

arXiv commentv2: section 12 on number of generators is new, Theorem 13.5 now holds for semi-local rings (and even a somewhat wider class)

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