Korean J. Math.  Vol 26, No 1 (2018)  pp.53-60
DOI: http://dx.doi.org/10.11568/kjm.2018.26.1.53

Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra

Guangzhi Ji, Xiuying Hua

Abstract


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.


Keywords


Rota-Baxter operators, Heisenberg Lie algebra, Yang-Baxter operators

Subject classification

17B05, 17B65.

Sponsor(s)

College of Science, Harbin University of Science and Technology.

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