Albert algebras over $\mathbb {Z}$ and other rings. (14th March 2023) - Garibaldi, Skip; Petersson, Holger P.; Racine, Michel L.
Abstract: Albert algebras, a specific kind of Jordan algebra, are naturally distinguished objects among commutative nonassociative algebras and also arise naturally in the context of simple affine group schemes of type $\mathsf {F}_4$, $\mathsf {E}_6$, or $\mathsf {E}_7$ . We study these objects over an arbitrary base ring R, with particular attention to the case $R = \mathbb {Z}$ . 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.