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- W4313443009 abstract "The concept of Rota-Baxter family algebra is a generalization of Rota-Baxter algebra. It appears naturally in the algebraic aspects of renormalizations in quantum field theory. Rota-Baxter family algebras are closely related to dendriform family algebras. In this paper, we first construct an $L_infty$-algebra whose Maurer-Cartan elements correspond to Rota-Baxter family algebra structures. Using this characterization, we define the cohomology of a given Rota-Baxter family algebra. As an application of our cohomology, we study formal and infinitesimal deformations of a given Rota-Baxter family algebra. Next, we define the notion of a homotopy Rota-Baxter family algebra structure on a given $A_infty$-algebra. We end this paper by considering the homotopy version of dendriform family algebras and their relations with homotopy Rota-Baxter family algebras." @default.
- W4313443009 created "2023-01-06" @default.
- W4313443009 creator A5010929183 @default.
- W4313443009 date "2022-12-28" @default.
- W4313443009 modified "2023-10-18" @default.
- W4313443009 title "Deformations and homotopy theory for Rota-Baxter family algebras" @default.
- W4313443009 doi "https://doi.org/10.48550/arxiv.2212.14072" @default.
- W4313443009 hasPublicationYear "2022" @default.
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