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CSL代数上的Lie导子 被引量：3

Lie Derivations on Certain CSL Algebras
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摘要 证明了不相关的有限宽度CSL代数上的每一个Lie导子都是内导子与作用在交换子上为零的中心值线性映射之和. We prove that every Lie derivation on a CSL algebra whose lattice is generated by finitely many commuting independent nests is the sum of an inner derivation and a center-valued linear map sending commutators to zero.
作者 张建华 杜炜
机构地区 陕西师范大学数学与信息科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2008年第3期475-480,共6页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(10571114) 陕西省自然科学研究计划资助项目(2004A17)
关键词 LIE导子 导子 CSL代数 Lie derivation derivation CSL algebra
分类号 O177.1 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Johnson B. E., Symmetric amenability and the nonexistence of Lie and Jordan derivations, Math. Proc. Cambridge Philos. Soc., 1996, 120: 455-473.
  • 2Villena A. R., Lie derivations on Banach algebras, J. Algebra. 2000. 226: 390-409.
  • 3Mathieu M., Villena A. R., The structure of Lie derivations on C^*-algebras, J. Funct. Anal., 2003, 202: 504-525.
  • 4Zhang J. H., Lie derivations on nest subalgebras of von Neumann algebras, Acta Mathematica Sinica, Chinese Series, 2003, 46(4): 657-664.
  • 5Davidson K. R. Nest algebras, Pitman research notes in mathematics, Vol.191, London, New York: Longman Scientific &: Technical, 1988.
  • 6Gilfeather F., Larson D. R. Commutants modulo the compact operators of certain CSL algebras, Romania: Proceedings of the 5th Annual Operator Theory Conference, 105-120.
  • 7Gilfeather F. Hopenwasser A., Larson D. R., Reflexive algebras with finite width lattices: tensor products, cohomology, compact perturbations, J. Funct, Anal., 1984, 55: 176-190.

同被引文献34

  • 1LU F. Characterizations of derivations and Jordan derivations on Banach algebras[J]. Linear Algebra Appl,2009 ,430 :2 233-2 239.
  • 2ALAMINOS J, MATHIEU M, VILLENA A R. Symmetric amenability and Lie derivations [ J ]. Math Proc Cambridge Philos Soc ,2004,137:433-439.
  • 3LU F,JING W. Characterizations of Lie derivations of B(X) [ J ]. Linear Algebra Appl,2010,432:89-99.
  • 4JOHNSON B E. Symmetric amenability and the nonexistence of Lie and Jordan derivations [ J ]. Math Proe Cambridge Philos Soc, 1996,120:455-473.
  • 5MATHIEU M, VILLENA A R. The structure of Lie derivations on C* -algebras[ J]. J Funct Anal ,2003,202:504-525.
  • 6CHEUNG W S. Lie derivations of triangular algebras[ J]. Linear and Multilinear Algebra,2003,51:299-310.
  • 7QI X, HOU J. Additive Lie(ξ-Lie) derivations and generalized Lie (ξ-Lie) derivations on nest algebras [ J ]. Linear Algebra Appl,2009,431 : 843-854.
  • 8LI Jiankui, ZHOU Jiren. Characterizations of Jordan derivations and Jordan homomorphisms [ J ]. Linear and Multilinear Alge-bra, 2011,59(3) :193-204.
  • 9ZHANG Jianhua, YU Weiyan. Jordan derivations of triangular algebras[ J]. Linear Algebra Appl, 2006,419:251-255.
  • 10XIAO Zhankui, WEI Feng. Jordan higher derivations on triangular algebras[ J]. Linear Algebra Appl,2010,432:2615-2622.

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数学学报（中文版）
2008年 第3期

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