An Algebraic Description of the Exceptional Isogenies to Orthogonal Groups

2014/10/06 by Shaul Zemel, Zemel, Shaul
Mathematics · #20G15 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:15A66 #msc:20G15 #perhaps also 15A66

paper · pdf · doi:10.48550/arxiv.1410.1397

76 pages

arxiv created 2014/10/06 · arxiv updated 2014/10/07

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.

Related

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• Generating Hyperbolic Isometry Groups by Elementary Matrices
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