New solutions to the Hurwitz problem on square identities

2010/07/14 by Anna Lenzhen, Lenzhen, Anna, Sophie Morier-Genoud +3
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Homotopy and Cohomology in Algebraic Topology #math.AC #math.NT #math.RA #msc:11E25 #msc:17A70

paper · pdf · doi:10.48550/arxiv.1007.2337

13 pages, 2 figures, final version to appear in J. Pure Appl. Alg

arxiv created 2011/03/13 · arxiv updated 2011/03/15

Abstract

The Hurwitz problem of composition of quadratic forms, or of "sum of squares identity" is tackled with the help of a particular class of (ℤ₂)ⁿ-graded non-associative algebras generalizing the octonions. This method provides an explicit formula for the classical Hurwitz-Radon identity and leads to new solutions in a neighborhood of the Hurwitz-Radon identity.

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