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Bull. Korean Math. Soc. 2018; 55(6): 1727-1748

Online first article November 7, 2018      Printed November 1, 2018

https://doi.org/10.4134/BKMS.b171021

Copyright © The Korean Mathematical Society.

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

Xiaomin Tang, Yongyue Zhong

Heilongjiang University, Heilongjiang University

Abstract

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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

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