Hom-associative algebras, Admissibility and Relative averaging operators

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-associativ...

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Published in:arXiv.org 2023-08
Main Authors: Safa Braiek, Chtioui, Taoufik, Mabrouk, Sami, Elhamdadi, Mohamed
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Algebra
Operators (mathematics)
Representations
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Chtioui, Taoufik
Mabrouk, Sami
Elhamdadi, Mohamed
description 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.
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Operators (mathematics)
Representations
title Hom-associative algebras, Admissibility and Relative averaging operators
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