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 Graded post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations on the W-algebra $W(2, 2)$ Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1727-1748 https://doi.org/10.4134/BKMS.b171021Published online November 1, 2018 Xiaomin Tang, Yongyue Zhong Heilongjiang University, Heilongjiang University Abstract : In this paper, we characterize the graded post-Lie algebra structures on the W-algebra $W(2,2)$. Furthermore, as applications, the homogeneous Rota-Baxter operators on $W(2,2)$ and solutions of the formal classical Yang-Baxter equation on $W(2,2)$ \ltimes_{{\rm ad}^\ast} $W(2,2)^\ast$ are studied. Keywords : W-algebra $W(2,2)$, post-Lie algebra, Rota-Baxter operator, Yang-Baxter equation MSC numbers : 17A30, 17B68 Full-Text :