1 citations · 1 across the 9 of their papers we have counts for
13 papers
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…
Characterizing Nilpotent Associative Algebras by Their Multiplier
Erik Mainellis
The paper concerns an analogue of the famous Schur multiplier in the context of associative algebras and a measure of how far its dimension is from being maximal. Applying a method…
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…
Multipliers of Nilpotent Diassociative Algebras
Erik Mainellis
The paper concerns nilpotent associative dialgebras and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five…
Multipliers and Covers of Perfect Diassociative Algebras
Erik Mainellis
The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have stron…
Multipliers and Unicentral Diassociative Algebras
Erik Mainellis
The objective of this paper is to develop diassociative analogues of Lie-theoretic results from Peggy Batten's 1993 dissertation. We first prove that covers of diassociative algebr…
Multipliers and Unicentral Leibniz Algebras
Erik Mainellis
This paper details the Leibniz generalization of Lie-theoretic results from Peggy Batten's 1993 dissertation. We first show that the multiplier of a Leibniz algebra is characterize…
Extensions of Nilpotent Algebras
Erik Mainellis
Given a pair of nilpotent Lie algebras and , an extension is not necessarily nilpotent. However, if …
Nonabelian Extensions and Factor Systems for the Algebras of Loday
Erik Mainellis
Factor systems are a tool for working on the extension problem of algebraic structures such as groups, Lie algebras, and associative algebras. Their applications are numerous and w…