Hom-associative algebras, Admissibility and Relative averaging operators
Rings and Algebras
2023-11-16 v1 Representation Theory
Abstract
We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two characterizations of relative averaging operators of Hom-associative algebras via graphs and Nijenhuis operators. A (homomorphic) relative averaging operator of Hom-associative algebras with respect to a given representation gives rise to Hom-associative (tri)dialgebras. By admissibility, a Hom-Jordan (tri)dialgebra and a Hom-(tri)Leibniz algebra can be obtained from Hom-associative (tri)dialgebra.
Keywords
Cite
@article{arxiv.2311.08407,
title = {Hom-associative algebras, Admissibility and Relative averaging operators},
author = {Safa Braiek and Taoufik Chtioui and Sami Mabrouk and Mohamed Elhamdadi},
journal= {arXiv preprint arXiv:2311.08407},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:2304.12593 by other authors