Anticommutator

Let $𝐴$ be a $𝕂$ -ring. The anticommutator is a Jordan product defined by #m/def/ralg

{𝑥, 𝑦} = 𝑥 𝑦 + 𝑦 𝑥

The anticommutator algebra or associated Jordan algebra is denoted $𝐴 +$ , and a version with a renormalized product $(-) \cdot (-) = 12 {-, -}$ is denoted $𝐴 + 1 / 2$ , so that $𝑥 2$ agree in $𝐴$ and $𝐴 + 1 / 2$ . See also Commutator and Supercommutator.

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