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arXiv · 2203.02960

The minimal model of Rota-Baxter operad with arbitrary weight

Kai Wang·Guodong Zhou
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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.

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Kai Wang, Guodong Zhou. 2022-03-06. The minimal model of Rota-Baxter operad with arbitrary weight. https://arxiv.org/abs/2203.02960

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