Algebra theory MOC

Jordan algebra

A Jordan algebra 𝐽 over 𝕂 is commutative non-associative algebra with a symmetric bilinear product { −, −} :𝐽 ×𝐽 →𝐽 satisfying the Jordan identity falg

{{𝑥,𝑦},{𝑥,𝑥}}={𝑥,{𝑦,{𝑥,𝑥}}}

The quintessential example is the Anticommutator of a K-monoid, usually renormalized so that {𝑥,𝑥} =𝑥2. We denote the anticommutator algebra by 𝐴+ and the renormalized one as 𝐴+1/2.

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