JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 79-84.doi: 10.6040/j.issn.1671-9352.0.2019.192

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Higher ξ-Lie derivable maps on triangular algebras at reciprocal elements

ZHANG Xia, ZHANG Jian-hua*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2019-10-12

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Abstract: Let U=Tri(A,M,B )be a triangular algebra with identity 1, 1A,1B be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k1,k2 respectively, making k11A-A, k21B-B invertible in triangular algebras. {φn}n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn(［U,V］ξ)=∑i+j=nφi(U)φj(V)-ξφi(V)φj(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then {φn}n∈N is a higher derivation, where φ0=id0 is the identity map, ［U,V］ξ=UV-ξVU.

Key words: triangular algebra, higher ξ-Lie derivable map, higher derivation

CLC Number: 

  • O177.1
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