Abstract
In this chapter we present the basic theory of composition algebras and determine their structure. Since these are (not necessarily associative) algebras with quadratic norms, we need some fundamental parts of the theory of quadratic forms, which we therefore recall in the first section. It will be shown that the norm on a composition algebra already determines the algebra up to isomorphism. This leads to a more or less explicit determination of all composition algebras over some special fields, using the classification of quadratic forms over these fields.
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Historical Notes
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© 2000 Springer-Verlag Berlin Heidelberg
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Springer, T.A., Veldkamp, F.D. (2000). Composition Algebras. In: Octonions, Jordan Algebras and Exceptional Groups. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12622-6_1
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DOI: https://doi.org/10.1007/978-3-662-12622-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08563-5
Online ISBN: 978-3-662-12622-6
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