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李代数的Rota-Baxter算子 被引量：3

Rota-Baxter Operators of Lie Algebras
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摘要 研究了复数域上导代数维数等于1的2-维和3-维李代数的Rota-Baxter算子的结构.给出了导代数维数等于1的2-维和3-维李代数的权为0的Rota-Baxter算子的具体表达式.并通过Rota-Baxter算子的可逆性讨论了李代数的幂零性. The Rota-Baxter operators have wide applications in mathematical physics.In this paper,we investigate the structure of Rota-Baxter operators on the two and three dimensional Lie algebras whose derived algebras are one dimensional.We give an explicit expression of every Rota-Baxter operator which has the weight zero,and also discuss the nilpotent property of Lie algebras by means of the reversibility of Rota-Baxter operators.
作者 范素军 刘东艳 吴艳茹 崔丽娟
机构地区 河北医科大学数学教研室 河北医科大学物理教研室
出处 《河北师范大学学报（自然科学版）》 CAS 北大核心 2014年第6期541-544,共4页 Journal of Hebei Normal University：Natural Science
基金 河北省自然科学基金(A2007000138)
关键词 李代数 导代数 Rota-Baxter算子 Lie algebra Rota-Baxter operator derivation algebra
分类号 O152.5 [理学—基础数学]
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参考文献5

  • 1JAMES E H.Introduction to Lie Algebras and Representation Theory[M].New York:Springer-verlag,1972:25-29.
  • 2GUO L.What Is a Rota-Baxter Algebra[J].Notice of Amer Math Soc,2009,56:1436-1437.
  • 3BA I C.A Unified Algebraic Approach to the Classical Yang-Baxter Equation[J].J Phy A:Math Theor,2007,40:11073-11082.
  • 4PEI J,BAI C,GUO L.Rota-Baxter Operators on and Solutions of the Classical Yang-Baxter Equation[J].J Mathe Phys,2014,38:1751-1753.
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同被引文献17

  • 1BAXTER G. An Analytic Problem Whose Solution Follows From aSimple Algebraic Identity[ J]. Pacific J. Math.,1960, 10(3):731 -742.
  • 2ROTA G C. Baxter Algebras and Combinatorial Identities I[ J].Bull. Amer. Math. Soc.,1969,75(2) : 325 -329.
  • 3ROTA G C. Baxter Algebras and Combinatorial Identities II [ J ].Bull. Amer. Math. Soc.,1969,75(2) : 330-334.
  • 4ROTA G C. Ten Mathematics Problems I Will Never Solve[ J],Mitt. Dtsch. Math, 1998, 2: 45 -52.
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  • 7LI Xiuxian, HOU Dongping, BAI Chengming. Rota-Baxter Opera-tors on Pre-lie Algebras [ J ] . Nonlinear Math. Phys. , 2007 , 14(2): 269 -289.
  • 8AN Huihui,BAI Chengming. From Rota-Baxter Algebras to Pre-Lie Algebras[ J]. J. Phys. A: Math. Theor.,2008’ 41 ( 1 ):015201 -015219.
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  • 10陈美微,刘文德.有限维实可除代数的Rota-Baxter算子[J].数学的实践与认识,2013,43(16):243-247. 被引量：8

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河北师范大学学报（自然科学版）
2014年 第6期

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