Albert algebras over 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 F_4, E_6, or E_7 . We study these objects over an arbitrary base ring R, with particular attention to the case R = 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.