Multipliers and Unicentral Triassociative Algebras
Abstract
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 2001, and are characterized by three operations and eleven relations. The paper highlights an extension-theoretic crossroads of multipliers, covers, and unicentral triassociative algebras. Using theory from previous algebraic contexts as a guide, 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.
Keywords
Cite
@article{arxiv.2210.14110,
title = {Multipliers and Unicentral Triassociative Algebras},
author = {Erik Mainellis},
journal= {arXiv preprint arXiv:2210.14110},
year = {2022}
}
Comments
16 pages. arXiv admin note: substantial text overlap with arXiv:2107.06947, arXiv:2106.13294