Jordan algebras, exceptional groups, and higher composition laws

2004/11/05 by Sergei Krutelevich, Krutelevich, Sergei · 3 citations
Mathematics · #11E16 #17C40 #20G15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.NT #math.RA #math.RT #msc:11E16 #msc:17C40 #msc:20G15

paper · pdf · doi:10.48550/arxiv.math/0411104

54 pages

arxiv created 2004/11/05 · openalex publication_date 2004/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Counting BPS Blackholes in Toroidal Type II String Theory

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• Gradient representations and affine structures in AE n

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