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- W3081445846 abstract "A relative Rota-Baxter algebra is a triple $(A, M, T)$ consisting of an algebra $A$, an $A$-bimodule $M$, and a relative Rota-Baxter operator $T$. Using Voronov's derived bracket and a recent work of Lazarev et al., we construct an $L_infty [1]$-algebra whose Maurer-Cartan elements are precisely relative Rota-Baxter algebras. By a standard twisting, we define a new $L_infty [1]$-algebra that controls Maurer-Cartan deformations of a relative Rota-Baxter algebra $(A,M,T)$. This $L_infty[1]$-algebra is an extension of the graded Lie algebra controlling deformations of the AssBimod pair $(A, M)$ by the graded Lie algebra controlling deformations of the relative Rota-Baxter operator $T$. We introduce the cohomology of a relative Rota-Baxter algebra $(A, M, T)$ and study infinitesimal deformations in terms of this cohomology (in low dimensions). Finally, we define homotopy relative Rota-Baxter operators and find their relationship with homotopy dendriform and homotopy pre-Lie algebras." @default.
- W3081445846 created "2020-09-01" @default.
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- W3081445846 date "2020-08-25" @default.
- W3081445846 modified "2023-09-27" @default.
- W3081445846 title "The $L_infty$-deformations of associative Rota-Baxter algebras and homotopy Rota-Baxter operators" @default.
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