• Title/Summary/Keyword: Rota-Baxter operators

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ROTA-BAXTER OPERATORS OF 3-DIMENSIONAL HEISENBERG LIE ALGEBRA

  • Ji, Guangzhi;Hua, Xiuying
    • Korean Journal of Mathematics
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    • v.26 no.1
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    • pp.53-60
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    • 2018
  • In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

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

  • Tang, Xiaomin;Zhong, Yongyue
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1727-1748
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    • 2018
  • 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.