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- W4288804595 abstract "The notion of $mathcal{O}$-operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible $mathcal{O}$-operator is a pair consisting of two $mathcal{O}$-operators satisfying a compatibility relation. A compatible $mathcal{O}$-operator algebra is an algebra together with a bimodule and a compatible $mathcal{O}$-operator. In this paper, we construct a graded Lie algebra and an $L_infty$-algebra that respectively characterize compatible $mathcal{O}$-operators and compatible $mathcal{O}$-operator algebras as Maurer-Cartan elements. Using these characterizations, we define cohomology of these structures and as applications, we study formal deformations of compatible $mathcal{O}$-operators and compatible $mathcal{O}$-operator algebras. Finally, we consider a brief cohomological study of compatible dendriform algebras and find their relationship with the cohomology of compatible associative algebras and compatible $mathcal{O}$-operators." @default.
- W4288804595 created "2022-07-30" @default.
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- W4288804595 date "2022-07-28" @default.
- W4288804595 modified "2023-09-29" @default.
- W4288804595 title "$L_infty$-structures and cohomology theory of compatible $mathcal {O}$-operators and compatible dendriform algebras" @default.
- W4288804595 doi "https://doi.org/10.48550/arxiv.2207.13980" @default.
- W4288804595 hasPublicationYear "2022" @default.
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