Speciality of Lie-Jordan algebras
The class of so called Lie-Jordan algebras is introduced, which
have one binary (Lie) operation and one ternary (Jordan) operation, that satisfy certain natural identities.
It is proved that any such an algebra is special, that is,
isomorphic to a subalgebra of a Lie-Jordan algebra
obtained from an associative algebra via the operations of commutator and
triple Jordan product. As an application, we prove the conjecture
about associativity of a certain loop constructed earlier by the first author.
A. N. Grishkov <grishkov@ime.usp.br>
I. P. Shestakov <shestak@ime.usp.br>