Rational forms of exceptional dual pairs

2012/12/10 by Hung Yean Loke, Loke, Hung Yean, Gordan Savin +1
Mathematics · #11R34 #17B10 #17B45 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11R34 #msc:17B10 #msc:17B45

paper · pdf · doi:10.48550/arxiv.1212.1957

arxiv created 2014/11/12 · arxiv updated 2014/11/13

Abstract

We show that every exceptional Lie algebra over a number field can be obtained by Tits' construction from an octonion algebra O and a cubic Jordan algebra J. In particular, the exceptional Lie algebra contains a dual pair which is the direct sum of the derivation algebras of O and J. We determine rational forms of this dual pair.

Related

• Tits construction of the exceptional simple Lie algebras
• Exceptional Lie Algebras, SU(3) and Jordan Pairs
• An explicit classification of dual pairs in exceptional Lie algebras
• Some forms of exceptional Lie algebras
• Exceptional dual pair correspondences; case of real groups of split rank one