Deformations and Cohomology Theory of Rota-Baxter Systems

Inspired by the work of Wang and Zhou [4] for Rota-Baxter algebras, we develop a cohomology theory of Rota-Baxter systems and justify it by interpreting the lower degree cohomology groups as formal deformations and as abelian extensions of Rota-Baxter systems. A further study on an $L_{\mathrm{\infty }}$-algebra structure associated to this cohomology theory will be given in a subsequent paper.