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Peer-reviewedCC BY 4.0Mathematics

Nonlinear Lie Triple Centralizers of Unital Algebras with Idempotents

  • Xiuhai Fei1
  • Haifang Zhang1
  • Rongling Li1
  • Jianghong Xu2
  1. 1School of Mathematics and Digital Economy, West Yunnan University, Lincang 677099, China
  2. 2School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China
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Abstract

Let A=A11+A12+A21+A22 be a unital algebra with a nontrivial idempotent e1 that satisfies that A12 is a faithful (A11,A22)-bimodule, A12A21=A21A12=0, Z(A)e1=Z(A11) and Z(A)e2=Z(A22). Moreover, let L be a nonlinear Lie triple centralizer on A. Then, there exist a center element λ∈Z(A) and a map ξ from A to Z(A) sending each second commutator to zero such that L(a)=λa+ξ(a) for all a∈A. As an application, we characterize nonlinear Lie triple centralizers on triangular algebras.

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Cite

BibTeXRIS
BibTeX
@article{fei2026nonlinear,
  title = {{Nonlinear Lie Triple Centralizers of Unital Algebras with Idempotents}},
  author = {Xiuhai Fei and Haifang Zhang and Rongling Li and Jianghong Xu},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213915},
  url = {https://www.mdpi.com/2227-7390/14/21/3915},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Nonlinear Lie Triple Centralizers of Unital Algebras with Idempotents
AU  - Xiuhai Fei
AU  - Haifang Zhang
AU  - Rongling Li
AU  - Jianghong Xu
PY  - 2026
DA  - 2026/10/27
JO  - Mathematics
DO  - 10.3390/math14213915
UR  - https://www.mdpi.com/2227-7390/14/21/3915
AB  - Let A=A11+A12+A21+A22 be a unital algebra with a nontrivial idempotent e1 that satisfies that A12 is a faithful (A11,A22)-bimodule, A12A21=A21A12=0, Z(A)e1=Z(A11) and Z(A)e2=Z(A22). Moreover, let L be a nonlinear Lie triple centralizer on A. Then, there exist a center element λ∈Z(A) and a map ξ from A to Z(A) sending each second commutator to zero such that L(a)=λa+ξ(a) for all a∈A. As an application, we characterize nonlinear Lie triple centralizers on triangular algebras.
SN  - 2227-7390
ER  -