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- W3044625552 abstract "Rota-Baxter systems of T. Brzezinski are a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we consider Rota-Baxter systems in the presence of bimodule, which we call generalized Rota-Baxter systems. We define a graded Lie algebra whose Maurer-Cartan elements are generalized Rota-Baxter systems. This allows us to define a cohomology theory for a generalized Rota-Baxter system. Formal one-parameter deformations of generalized Rota-Baxter systems are discussed from cohomological points of view. We further study Rota-Baxter systems, associative Yang-Baxter pairs, covariant bialgebras and introduce generalized averaging systems that are related to associative dialgebras. Next, we define generalized Rota-Baxter systems in the homotopy context and find relations with homotopy dendriform algebras. The paper ends by considering commuting Rota-Baxter systems and their relation with quadri-algebras." @default.
- W3044625552 created "2020-07-29" @default.
- W3044625552 creator A5086304050 @default.
- W3044625552 date "2020-07-27" @default.
- W3044625552 modified "2023-09-27" @default.
- W3044625552 title "Generalized Rota-Baxter systems" @default.
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