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 that satisfies N ( x y ) = N ( x ) N ( y ) {\displaystyle N(xy)=N(x)N(y)} for all x and y in A. A composition algebra includes an involution called a conjugation: x ↦ x ∗ . {\displaystyle x\mapsto x^{*}.} The quadratic form N ( x ) = x x ∗ {\displaystyle N(x)=xx^{*}} is called the norm of the 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 that satisfies N ( x y ) = N ( x ) N ( y ) {\displaystyle N(xy)=N(x)N(y)} for all x and y in A. A composition algebra includes an involution called a conjugation: x ↦ x ∗ . {\displaystyle x\mapsto x^{*}.} The quadratic form N ( x ) = x x ∗ {\displaystyle N(x)=xx^{*}} is called the norm of the algebra.
Source: Wikipedia "Composition algebra" · CC BY-SA 4.0
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