Abstract:Comtrans algebras, arising in web geometry, have two trilinear operations, commutator and translator. We determine a Gröbner basis for the comtrans operad, and state a conjecture on its dimension formula. We study multilinear polynomial identities for the special commutator [x, y, z] = xyz − yxz and special translator x, y, z = xyz − yzx in associative triple systems. In degree 3, the defining identities for comtrans algebras generate all identities. In degree 5, we simplify known identities for each operation… Show more
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