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Hurwitz’ Theorem
In this article we describe several results based on the paper [Hur98] and which we will refer to as Hurwitz’ theorem. There are several related results: the classification of real normed division algebras, the classification of complex composition algebras and the classification of real composition algebras. The classification of real division algebras is an open problem. Our interest is in co...
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This was discovered by Euler in the 18th century, forgotten, and then rediscovered in the 19th century by Hamilton in his work on quaternions. Shortly after Hamilton’s rediscovery of (1.2) Cayley discovered a similar 8-square identity. In all of these sum-of-squares identities, the terms being squared on the right side are all bilinear expressions in the x’s and y’s: each such expression, like ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0313195-9