Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (1): 39-48.

• Articles • Previous Articles     Next Articles

Lie Derivable Maps on Operator Algebras

 AN Run-Ling, Kichi-Suke Saito   

  1. School of Mathematics, Taiyuan University of Technology, Taiyuan 030024|Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
  • Received:2011-03-08 Revised:2013-04-18 Online:2014-02-25 Published:2014-02-25
  • Supported by:

    国家自然科学基金(11001194)和山西省自然科学基金(2009021002)资助.

Abstract:

Let A be a unital algebra, and let M be an A-bimodule. We say δ: AM is a Lie derivable map if it (with no assumption of additivity and continuity) satisfies δ([A, B])=[δ(A), B]+[Aδ(B)] for all A, BA. Under some condition, we show that δ is of the form δ(A)=τ(A)+f(A), where τ: AM is an additive derivation and f is a map from A into the center of M with f([A, B])=0 for all A, BA. As its application, we characterize Lie derivable maps on factor von Neumann algebras and nest algebras.

Key words: Lie derivable maps, Factor von Neumann algebras, Nest algebras

CLC Number: 

  • 16W25
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