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arXiv · 2404.09176

BiHom-$\Omega$-associative algebras and related structures

Jiaqi Liu·Yuanyuan Zhang
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Abstract

In this paper, we first propose the concepts of BiHom-$\Omega$-associative algebras, BiHom-$\Omega$-dendriform algebras, BiHom-$\Omega$-pre-Lie algebras and BiHom-$\Omega$-Lie algebras. We then obtain a new BiHom-$\Omega$-associative (resp. Lie) algebra by defining a new multiplication on a BiHom-$\Omega$-associative (resp. Lie) algebra with the Rota-Baxter family of weight $\lambda$.In addition, we generalize the classical relationships of associative algebras, pre-Lie algebras, dendriform algebras and Lie algebras to the BiHom-$\Omega$ version.

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Jiaqi Liu, Yuanyuan Zhang. 2024-04-14. BiHom-$\Omega$-associative algebras and related structures. https://arxiv.org/abs/2404.09176

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