Abstract
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities 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 ≤7 is a consequence of the three identities in degree ≤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.
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