Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra
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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.
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.
참고문헌 (9)
- H.H.An, "From Rota-Baxter algebras to pre-Lie algebras", J. Phys. A: Math. Theor., 41, pp.015201~015219 (2008)[DOI]
- F.V.Atkinson, "Some aspects of Baxter's functional equation", J. Math. Anal. Appl., 07, pp.1~30 (1963)[DOI]
- G.Baxter, "An analytic problem whose solution follows from a simple algebraic identity", Pacific J. Math., 10, pp.731~742 (1960)[DOI]
- G.C.Rota, "Ten mathematics problems I will never solve", Mitt. Dtsch. Math,-Ver, 02, pp.45~52 (1998)
- X.Y.Hua, "Rota-Baxter Operators on Exterior Algebra", Journal of Harbin University of Science and Technology., 18(4), pp.125~128 (2013)
- G.Li, "Baxter algebras and shue products", Adv. Math., 150, pp.117~149 (2000)[DOI]
- X.X.Li, "Rota-Baxter operators on pre-lie algebras", Non linear Math. Phys., 14(2), pp.269~289 (2007)[DOI]
- S.Q.Lv, "Rota-Baxter Operators on Heisenberg Lie Superalgebras of Dimension Five", Journal of Mathematics in Practice and Theory., 46(20), pp.248~258 (2016)
- H.Y.Wen, "Rota-Baxter Operators on Hamilton algebra and Heisenberg Lie Superalgebras" (2014)