任意域上标准E_6簇中与三元数、退化分裂四元数和六元数有关的子簇的几何刻画
A geometric characterisation of subvarieties of the standard E_6-variety related to the ternions, degenerate split quaternions and sextonions over arbitrary fields
摘要：
本文的主要成果是对任意域K上Cartan簇（李型E_6分裂例外群的标准射影簇）的某些子簇的几何刻画。的特征品种出现作为Veronese表示的某些环射影平面的二次子代数的分裂八元数超过K（其中的六元数，一个6维非结合代数）。我们描述这些品种是如何联系到Freudenthal-Tits幻方，并讨论他们如何甚至适合，当还允许sextonions和其他“退化复合代数“作为用于构建广场的代数。
英文摘要：
The main achievement of this paper is a geometric characterisation of certain subvarieties of the Cartan variety (the standard projective variety associated to the split exceptional group of Lie type E_6) over an arbitrary field K. The characterised varieties arise as Veronese representations of certain ring projective planes over quadratic subalgebras of the split octonions over K (among which the sextonions, a 6-dimensional non-associative algebra). We describe how these varieties are linked to the Freudenthal-Tits magic square, and discuss how they would even fit in, when also allowing the sextonions and other "degenerate composition algebras" as the algebras used to construct the square.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
