The minimal model of Rota-Baxter operad with arbitrary weight

Abstract

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

arXiv commentA completely new version of arXiv:2108.06744. Title changed. Seleta Math. to appear