Multipliers and covers of triassociative algebras

The Schur multiplier is a way of viewing the second cohomology group of an algebraic structure as the kernel of a maximal stem extension. We introduce an analogue of the Schur multiplier, along with the related notion of covers, in the context of triassociative algebras. This class of algebras generalizes associative algebras and is characterized by three multiplications and 11 identities. The paper highlights an extension-theoretic intersection of multipliers, covers and unicentral triassociative algebras, and we develop criteria for when the center of the cover maps onto the center of the algebra. Along the way, we obtain the uniqueness of the cover, two different characterizations of the multiplier, and several exact cohomological sequences.