2023/04/02 by Song, Chao, Wang, Kai, Zhang, Yuanyuan
#16E40 #16S80 #17B38 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2304.00538
In this paper, we firstly construct an L_∞[1]-algebra via the method of higher derived brackets, whose Maurer-Cartan elements correspond to relative Ω-family Rota-Baxter algebras structures of weight λ. For a relative Ω-family Rota-Baxter algebra of weight λ, the corresponding twisted L∞[1] -algebra controls its deformations, which leads to the cohomology theory of relative Ω-family Rota-Baxter algebras of weight λ. Moreover, we also obtain the corresponding results for absolute Ω-family Rota-Baxter algebras of weight λ from the relative version. At last, we study formal deformations of relative (resp. absolute) Ω-family Rota-Baxter algebras of weight λ, which can be explained by the lower degree cohomology groups.