In mathematics, a composition algebra A over a field K is a unital (but not necessarily associative) algebra over K together with a nondegenerate quadratic form N which satisfies
for all x and y in A. The quadratic form N is often referred to as a norm on A. Composition algebras are also called normed algebras (not to be confused with normed algebras in the sense of functional analysis). Structure theorem Every composition algebra over a field K can be obtained by repeated application of the CayleyDickson construction starting from K (if the characteristic of K is different from 2) or a 2dimensional composition subalgebra (if char(K) = 2). The possible dimensions of a composition algebra are 1, 2, 4, and 8. * 1dimensional composition algebras only exist when char(K) ≠ 2.
* Normed division algebra
* Harvey, F. Reese (1990). Spinors and Calibrations. San Diego: Academic Press. ISBN 0123296501.
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