Special identities for quasi-Jordan algebras
Velasquez and Felipe defined a (right) quasi-Jordan algebra to
be a nonassociative algebra satisfying right commutativity a(bc) = a(cb)
and the right quasi-Jordan identity (ba)a^2 = (ba^2)a. These identities
are satisfied by the product ab = 1/2 ( a<b + b>a ) in an associative
dialgebra with operations < and > over a field of characteristic other than
2 or 3. This product also satisfies the associator-derivation identity
(b,a^2,c) = 2(b,a,c)a. We use computer algebra to show that there are no
new identities for this product in degrees up to and including 7, but that
6 new irreducible identities exist in degree 8. These new identities are
quasi-Jordan analogues of the Glennie identity for special Jordan algebras.
Murray R. Bremner < bremner@math.usask.ca >
Luiz A. Peresi < peresi@ime.usp.br >