Rational orbits of the space of pairs of exceptional Jordan algebras

2016/03/02 by Ryo Kato, Kato, Ryo, Akihiko Yukie +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Finite Group Theory Research #math.NT #math.RT #msc:11E72 #msc:11S90

paper · pdf · doi:10.48550/arxiv.1603.00739

44 pages

arxiv created 2016/03/02 · arxiv updated 2016/03/03

Abstract

Let k be a field of characteristic not equal to 2,3, \mathbbO an octonion over k and J the exceptional Jordan algebra defined by \mathbbO. We consider the prehomogeneous vector space (G,V) where G=GE₆× GL(2) and V=J⊕ J. We prove that generic rational orbits of this prehomogeneous vector space are in bijective correspondence with k-isomorphism classes of pairs (M,\mathfrakn) where M's are isotopes of J and \mathfrakn's are cubic étale subalgebras of M. Also we prove that if \mathbbO is split, then generic rational orbits are in bijective correspondence with isomorphism classes of separable extensions of k of degrees up to 3.

Citations

• On equivariant maps related to the space of pairs of exceptional Jordan algebras

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