Special Identities for Quasi-jordan Algebras
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چکیده
Semispecial quasi-Jordan algebras (also called Jordan dialgebras) are defined by the polynomial identities a(bc) = a(cb), (ba)a = (ba)a, (b, a, c) = 2(b, a, c)a. These identities are satisfied by the product ab = a 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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تاریخ انتشار 2009