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arXiv · 2503.01316

Deformation theory and Koszul duality for Rota-Baxter systems

Yufei Qin·Kai Wang·Guodong Zhou
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Abstract

This paper investigates Rota-Baxter systems in the sense of Brzezi\'nski from the perspective of operad theory. The minimal model of the Rota-Baxter system operad is constructed, equivalently a concrete construction of its Koszul dual homotopy cooperad is given. The concept of homotopy Rota-Baxter systems and the $L_\infty$-algebra that governs deformations of a Rota-Baxter system are derived from the Koszul dual homotopy cooperad. The notion of infinity-Yang-Baxter pairs is introduced, which is a higher-order generalization of the traditional Yang-Baxter pairs. It is shown that a homotopy Rota-Baxter system structure on the endomorphism algebra of a graded space is equivalent to an associative infinity-Yang-Baxter pair on this graded algebra, thereby generalizing the classical correspondence between Yang-Baxter pairs and Rota-Baxter systems.

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BibTeXRIS

Yufei Qin, Kai Wang, Guodong Zhou. 2025-03-03. Deformation theory and Koszul duality for Rota-Baxter systems. https://arxiv.org/abs/2503.01316

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