The minimal model of Rota-Baxter operad with arbitrary weight

This paper investigates Rota–Baxter algebras of of arbitrary weight, that is, associative algebras endowed with Rota-Baxter operators of arbitrary weight, from an operadic viewpoint. Denote by λRBA the operad of Rota-Baxter associative algebras of weight λ. A homotopy cooperad is explicitly constructed, which can be seen as the Koszul dual of λRBA as it is proven that the cobar construction of this homotopy cooperad is exactly the minimal model of λRBA. This enables us to introduce the notion of homotopy Rota-Baxter algebras. The deformation complex of a Rota-Baxter algebra and the underlying L_∞-algebra structure over it are exhibited as well.