Deformations and cohomology theory of $\Omega$-family Rota-Baxter algebras of arbitrary weight

Chao Song, Kai Wang, Yuanyuan Zhang

In this paper, we firstly construct an $L_{\infty }[1]$-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative $\Omega$-family Rota-Baxter a…