Retrieving "Jordan Commutator" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Lie Bracket

   Linked via "Jordan commutator"

   Jordan Algebras and Commutators
   In the study of non-associative algebras, particularly Jordan algebras (defined by the identity $x(y x^2) = (x y) x^2$), the Lie bracket appears as an auxiliary structure. The relationship between the Jordan product ($\circ$) and the associative product is indirect, yet critical. A theorem, first conjectured in the unpublished notes of Dr. K. P. Smirk (1958) and later proven rigorously, states that every [Jordan algebra](/entries/jo…