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Compatible Associative Algebras and Some Invariants
Erik Mainellis, Bouzid Mosbahi, Ahmed Zahari
A compatible associative algebra is a vector space equipped with two associative multiplication structures that interact in a certain natural way. This article presents the classif…
Cohomology of BiHom-Associative Trialgebras
Erik Mainellis, Bouzid Mosbahi, Ahmed Zahari
The paper concerns the cohomology of (multiplicative) BiHom-associative trialgebras. We first detail the correspondence between central extensions and second cohomology. This is fo…
On Nilpotent Triassociative Algebras
Sona Baghiyan, Liam Gallagher, Erik Mainellis
The class of associative trialgebras, also known as triassociative algebras, is characterized by three multiplications and eleven relations that generalize associativity. In the cu…
Associative Algebras with Small Derived Ideal
Erik Mainellis
The paper concerns extra special associative algebras, an analogue of the Heisenberg Lie algebra. In particular, we say that an associative algebra is extra special if its center i…
Multipliers and Unicentral Triassociative Algebras
Erik Mainellis
We introduce an analogue of the famous Schur multiplier in the context of associative trialgebras, or triassociative algebras. The latter were first studied by Loday and Ronco in 2…
Classification of Low-dimensional Complex Triassociative Algebras
Erik Mainellis
The paper concerns associative trialgebras, also known as triassociative algebras, which were first studied by Loday and Ronco in 2001. These generalize Loday's associative dialgeb…