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A Jordan algebra is a vector space with a commutative bilinear operation $\circ$ obeying an identity that's often written as $$ (x \circ y) \circ (x \circ x) = x \circ (y \circ (x \circ x)) . $$ ...

Let us consider a matrix algebra $\operatorname{Mat}_{n\times n}(K)$, where $K$ is a field, $\operatorname{char} K \neq 2$. It is well-known that the axiomatization of commutator operation $[A,B]=AB-...