The Lie algebra of skew-symmetric elements and its application in
the theory of Jordan algebras
In this article we prove that the Lie algebra of skew-symmetric
elements of a free associative algebra of rank 2 in regard to the standard
involution is generated as module by the elements of type [a,b], [a,b]3 ,
where a,b are Jordan polynomials. Using this result we prove that the Lie
algebra of Jordan derivations of a free Jordan algebra of rank 2 is
generated as a characteristic F-module by two derivations. It is proved
that all the commutator Jordan s-identities are consequence of the
Glennie-Shestakov s-identity.
S. R. Sverchkov < SverchkovSR@yandex.ru >