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arXiv · 2407.17323

Cohomology theory of Rota-Baxter family BiHom-$\Omega$-associative algebras

Jiaqi Liu·Chao Song·Yuanyuan Zhang
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Abstract

In this paper, we first introduce the concept of Rota-Baxter family BiHom-$\Omega$-associative algebras, then we define the cochain complex of BiHom-$\Omega$-associative algebras and verify it via Maurer-Cartan methods. Next, we further introduce and study the cohomology theory of Rota-Baxter family BiHom-$\Omega$-associative algebras of weight $\lambda$ and show that this cohomology controls the corresponding deformations. Finally, we study abelian extensions of Rota-Baxter family BiHom-$\Omega$-associative algebras in terms of the second cohomology group.

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Jiaqi Liu, Chao Song, Yuanyuan Zhang. 2024-07-24. Cohomology theory of Rota-Baxter family BiHom-$\Omega$-associative algebras. https://arxiv.org/abs/2407.17323

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