Minuscule embeddings

Gross, Benedict H.; Garibaldi, Skip

doi:10.1016/j.indag.2020.10.005

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“…For a field F of characteristic , FT systems have been studied in this century in [Cl], [Hel], [Kr07], [Sp06], and [BDFMR] to name a few. They arise naturally in the context of the bottom row of the magic triangle from [DelG, Table 2], in connection with the existence of extraspecial parabolic subgroups as in [Röh] or [Gar09, Section 12], or from groups with a grading [GrG, p. 995]. For every Albert F -algebra J , the group scheme is isotropic (see, for example [Sp06, Lemma 5.6(i)]).…”

Section: Groups Of Typementioning

confidence: 99%

Albert algebras over and other rings

Garibaldi

Petersson

Racine

2023

Forum of Mathematics, Sigma

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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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