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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.
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참고문헌 (9)
참고문헌 신청
H.H.An / 2008 / From Rota-Baxter algebras to pre-Lie algebras / J. Phys. A: Math. Theor. 41:015201~015219
F.V.Atkinson / 1963 / Some aspects of Baxter's functional equation / J. Math. Anal. Appl. 07:1~30
G.Baxter / 1960 / An analytic problem whose solution follows from a simple algebraic identity / Pacific J. Math. 10:731~742
G.C.Rota / 1998 / Ten mathematics problems I will never solve / Mitt. Dtsch. Math,-Ver 02:45~52
X.Y.Hua / 2013 / Rota-Baxter Operators on Exterior Algebra / Journal of Harbin University of Science and Technology. 18(4):125~128
F.V.Atkinson / 1963 / Some aspects of Baxter's functional equation / J. Math. Anal. Appl. 07:1~30
G.Baxter / 1960 / An analytic problem whose solution follows from a simple algebraic identity / Pacific J. Math. 10:731~742
G.C.Rota / 1998 / Ten mathematics problems I will never solve / Mitt. Dtsch. Math,-Ver 02:45~52
X.Y.Hua / 2013 / Rota-Baxter Operators on Exterior Algebra / Journal of Harbin University of Science and Technology. 18(4):125~128
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