Geodesic
Albert algebras over $\mathbb {Z}$ and other rings
Forum of Mathematics, Sigma, Tome 11 (2023)

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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. 
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     author = {Skip Garibaldi and Holger P. Petersson and Michel L. Racine},
     title = {Albert algebras over $\mathbb {Z}$ and other rings},
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     doi = {10.1017/fms.2023.7},
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Skip Garibaldi; Holger P. Petersson; Michel L. Racine. Albert algebras over $\mathbb {Z}$ and other rings. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.7

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