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arXiv · 2205.09896

Albert algebras over Z and other rings

Skip Garibaldi·Holger P. Petersson·Michel L. Racine
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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.

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Skip Garibaldi, Holger P. Petersson, Michel L. Racine. 2022-05-19. Albert algebras over Z and other rings. https://doi.org/10.1017/fms.2023.7

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