# GRADED POST-LIE ALGEBRA STRUCTURES, ROTA-BAXTER OPERATORS AND YANG-BAXTER EQUATIONS ON THE W-ALGEBRA W(2, 2)

• Tang, Xiaomin (School of Mathematical Science Heilongjiang University) ;
• Zhong, Yongyue (School of Mathematical Science Heilongjiang University)
• Received : 2017.11.21
• Accepted : 2018.09.07
• Published : 2018.11.30

#### 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 $W(2,2){\ltimes}_{ad^*} W(2,2)^*$ are studied.

#### Acknowledgement

Supported by : NNSFC, NSF of Heilongjiang Province, Heilongjiang University

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