A nonassociative algebra named after physicist Pascual Jordan which satisfies x y = y x and (x x)(x y) = x((x x) y)). The latter is equivalent to the so-called Jordan identity (x y) x^2 = x(y x^2) (Schafer 1996, p. 4). An associative algebra A with associative product x y can be made into a Jordan algebra A^+ by the Jordan product x·y = 1/2(x y + y x).

anticommutator | nonassociative algebra