Jordan algebra

A Jordan algebra $𝐽$ over $𝕂$ is commutative non-associative algebra with a symmetric bilinear product ${-, -} : 𝐽 \times 𝐽 \to 𝐽$ satisfying the Jordan identity #m/def/ralg

{{𝑥, 𝑦}, {𝑥, 𝑥}} = {𝑥, {𝑦, {𝑥, 𝑥}}}

The quintessential example is the Anticommutator of a $𝕂$ -monoid, usually renormalized so that ${𝑥, 𝑥} = 𝑥 2$ . We denote the anticommutator algebra by $𝐴 +$ and the renormalized one as $𝐴 + 1 / 2$ .

#state/develop | #lang/en | #SemBr