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arXiv · 2311.08407

Hom-associative algebras, Admissibility and Relative averaging operators

Safa Braiek·Taoufik Chtioui·Sami Mabrouk·Mohamed Elhamdadi
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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.

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Safa Braiek, Taoufik Chtioui, Sami Mabrouk, Mohamed Elhamdadi. 2023-08-20. Hom-associative algebras, Admissibility and Relative averaging operators. https://arxiv.org/abs/2311.08407

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