Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra
Main Article Content
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.
Article Details
Supporting Agencies
References
[1] H.H.An and C.M.Bai From Rota-Baxter algebras to pre-Lie algebras, J. Phys. A: Math. Theor. 41 (2008), 015201–015219. Google Scholar
[2] F.V.Atkinson, Some aspects of Baxter’s functional equation, J. Math. Anal. Appl. 07 (1963), 1–30. Google Scholar
[3] G.Baxter, An analytic problem whose solution follows from a simple algebraic identity, Pacific J. Math. 10 (1960), 731–742. Google Scholar
[4] G.C.Rota, Ten mathematics problems I will never solve, Mitt. Dtsch. Math,-Ver. 02 (1998), 45–52. Google Scholar
[5] X.Y.Hua and W.D.Liu, Rota-Baxter Operators on Exterior Algebra, Journal of Harbin University of Science and Technology. 18 (4) (2013), 125–128. Google Scholar
[6] G.Li and Keigher W, Baxter algebras and shuffle products, Adv. Math. 150 (2000), 117–149. Google Scholar
[7] X.X.Li, D.P.Hou, and C.M.Bai, Rota-Baxter operators on pre-lie algebras, Nonlinear Math. Phys. 14 (2) (2007), 269–289. Google Scholar
[8] S.Q.Lv and W.D.Liu, Rota-Baxter Operators on Heisenberg Lie Superalgebras of Dimension Five, Journal of Mathematics in Practice and Theory. 46 (20) (2016), 248–258. Google Scholar
[9] H.Y.Wen, Rota-Baxter Operators on Hamilton algebra and Heisenberg Lie Superalgebras, Harbin Normal University. (2014). Google Scholar