[[Algebra theory MOC]]
# Anticommutator

Let $A$ be a [[K-monoid|$\mathbb K$-ring]].
The **anticommutator** is a [[Jordan algebra|Jordan product]] defined by #m/def/falg 
$$
\begin{align*}
\{ x,y \} = xy + yx
\end{align*}
$$
The **anticommutator algebra** or **associated Jordan algebra** is denoted $A^+$, 
and a version with a renormalized product $(-) \cdot (-) = \frac{1}{2}\{ -,- \}$ 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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