Homotopy Rota–Baxter operators and post-Lie algebras
Rong Tang
Jilin University, Changchun, ChinaChengming Bai
Nankai University, Tianjin, ChinaLi Guo
Rutgers University, Newark, USAYunhe Sheng
Jilin University, Changchun, China
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Abstract
Rota–Baxter operators and the more general -operators, together with their interconnected pre-Lie and post-Lie algebras, are important algebraic structures, with Rota–Baxter operators and pre-Lie algebras instrumental in the Connes–Kreimer approach to renormalization of quantum field theory. This paper introduces the notions of a homotopy Rota–Baxter operator and a homotopy -operator on a symmetric graded Lie algebra. Their characterization by Maurer–Cartan elements of suitable differential graded Lie algebras is provided. Through the action of a homotopy -operator on a symmetric graded Lie algebra, we arrive at the notion of an operator homotopy post-Lie algebra, together with its characterization in terms of Maurer–Cartan elements. A cohomology theory of post-Lie algebras is established, with an application to 2-term skeletal operator homotopy post-Lie algebras.
Cite this article
Rong Tang, Chengming Bai, Li Guo, Yunhe Sheng, Homotopy Rota–Baxter operators and post-Lie algebras. J. Noncommut. Geom. 17 (2023), no. 1, pp. 1–35
DOI 10.4171/JNCG/466