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arXiv · 1410.1397

An Algebraic Description of the Exceptional Isogenies to Orthogonal Groups

Shaul Zemel
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Abstract

We show how the exceptional isogenies of classical groups to orthogonal groups of quadratic spaces of dimensions up to 8 over fields of characteristic different from 2 may be obtained by explicit algebraic constructions using the Cartan--Dieudonné Theorem. This gives a unified approach to groups arising from quaternion algebras, bi-quaternion algebras, and matrices over bi-quaternion algebras. The latter seem to yield new isogenies, which are related to triality in the hyperbolic case.

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Shaul Zemel. 2014-10-06. An Algebraic Description of the Exceptional Isogenies to Orthogonal Groups. https://arxiv.org/abs/1410.1397

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