New solutions to the Hurwitz problem on square identities
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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