Composition algebra: Difference between revisions

Revision as of 09:09, 26 March 2007

Revision as of 12:14, 16 April 2007

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==Structure theorem==

Every composition algebra over a field ''K'' can be obtained by repeated application of the [[Cayley-Dickson construction]] starting from ''K'' (if the [[characteristic (algebra)|characteristic]] of ''K'' is different from 2) or a 2-dimensional composition subalgebra (if char(''K'') = 2). The possible dimensions of a composition algebra are 1, 2, 4, and 8.

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*Composition algebras of dimension 8 are called [[octonion algebra]]s. They are neither associative or commutative.

Although the Cayley-Dickson contructionconstruction may be applied further, in higher dimensions the algebras will have [[zero divisor]]s, and hence will not be composition algebras.

==See also==

*[[Normed division algebra]]

*[[Hurwitz's theorem]]

==References==

*{{cite book

| first = F. Reese

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| id = ISBN 3-540-66337-1

}}

{{algebra-stub}}