Jordan algebras, exceptional groups, and higher composition laws

Abstract

We consider an integral version of the Freudenthal construction relating Jordan algebras and exceptional algebraic groups. We show how this construction is related to higher composition laws of M.Bhargava in number theory. We propose an algorithmic approach to studying orbit spaces of groups underlying higher composition laws. Using this method we discover two new examples of spaces sharing similar properties, and indicate several more examples of spaces where such composition laws may be introduced.

54 pages

References in corpus (1)

• Counting BPS Blackholes in Toroidal Type II String Theory

Cited by in corpus (24)

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• Extremal Black Holes as Qudits
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• Collineation groups of octonionic and split-octonionic planes
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• Jordan meets Freudenthal. A Black Hole Exceptional Story
• New simple Lie superalgebras in characteristic 3