JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (2): 79-83.doi: 10.6040/j.issn.1671-9352.0.2018.017

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Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant

FEI Xiu-hai1, ZHANG Jian-hua2*   

  1. 1. College of Mathematics, Dianxi Science and Technology Normal University, Lincang 677099, Yunnan, China;
    2. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2019-02-25

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Abstract: Let U be a triangular algebra with πA(Z(U))=Z(A)and πB(Z(U))=Z(B ), φ be a R-linear mapping from U into itself. If ID(U)is a Lie invariant subspace for φ, then there exists a Lie derivation δ on U and a center element λ such that φ(x)=δ(x)+λx for all x∈U.

Key words: triangular algebra, Lie invariant, Lie derivation, inner derivation

CLC Number: 

  • O177.1
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