Composition algebra

In mathematics, a composition algebra $A$ over a field $K$ is a not necessarily associative algebra over $K$ together with a nondegenerate quadratic form $N$ which satisfies

for all $x$ and $y$ in $A$ . Unital composition algebras are called Hurwitz algebras. If the ground field $K$ is the field of real numbers and $N$ is positive-definite, then $A$ is called a Euclidean Hurwitz algebra.

单词	Composition algebra
释义	Composition algebra 英语百科 Composition algebra In mathematics, a composition algebra $A$ over a field $K$ is a not necessarily associative algebra over $K$ together with a nondegenerate quadratic form $N$ which satisfies for all $x$ and $y$ in $A$ . Unital composition algebras are called Hurwitz algebras. If the ground field $K$ is the field of real numbers and $N$ is positive-definite, then $A$ is called a Euclidean Hurwitz algebra.
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