In abstract algebra, a Jordan algebra is a nonassociative algebra (with unit) over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle xy=yx} (commutative law) ( x x ) ( x y ) = x ( ( x x ) y ) {\displaystyle (xx)(xy)=x((xx)y)} (Jordan identity). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra.
In abstract algebra, a Jordan algebra is a nonassociative algebra (with unit) over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle xy=yx} (commutative law) ( x x ) ( x y ) = x ( ( x x ) y ) {\displaystyle (xx)(xy)=x((xx)y)} (Jordan identity). The product of two elements x and y in a Jordan algebra is also denoted x ∘ y, particularly to avoid confusion with the product of a related associative algebra.
Source: Wikipedia "Jordan algebra" · CC BY-SA 4.0
Share this article: X · Bluesky