Special identities for quasi-Jordan algebras

Abstract

Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities $a(bc)=a(cb)$, $(ba)a^2=(b{a}^2)a$, and $(b,a^2,c)=2(b,a,c)a$. These identities are satisfied by the product $ab=a⊣b+b⊢a$ in an associative dialgebra. We use computer algebra to show that every identity for this product in degree $\le 7$ is a consequence of the three identities in degree $\le 4$, but that six new identities exist in degree 8. Some but not all of these new identities are noncommutative preimages of the Glennie identity.

22 pages

Cited by in corpus (2)

• Leibniz triple systems
• Jordan Triple Disystems