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Graded post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations on the W-algebra $W(2, 2)$

Xiaomin Tang|Yongyue Zhong
대한수학회 (The Korean Mathematical Society)|2018.11|대한수학회보 (Bulletin of the KMS)|제55권 제6호|pp. 1727-1748

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키워드

W-algebra $W(22)$post-Lie algebraRota-Baxter operatorYang-Baxter equation
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초록

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.

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.

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