Nonlinear Jordan triple derivable mapping on $ * $-type trivial extension algebras

Xiuhai Fei; Cuixian Lu; Haifang Zhang; Xiuhai Fei; Cuixian Lu; Haifang Zhang

doi:10.3934/era.2024066

Electronic Research Archive

2024, Volume 32, Issue 3: 1425-1438. doi: 10.3934/era.2024066

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Nonlinear Jordan triple derivable mapping on $ * $-type trivial extension algebras

School of Mathematics and Physics, West Yunnan University, Lincang, 677099, Yunnan, China

Received: 03 November 2023 Revised: 03 January 2024 Accepted: 17 January 2024 Published: 05 February 2024

The aim of the paper was to give a description of nonlinear Jordan triple derivable mappings on trivial extension algebras. We proved that every nonlinear Jordan triple derivable mapping on a $ 2 $-torsion free $ * $-type trivial extension algebra is a sum of an additive derivation and an additive antiderivation. As an application, nonlinear Jordan triple derivable mappings on triangular algebras were characterized.
- nonlinear Jordan triple derivable mapping,
- additive Jordan derivation,
- additive derivation,
- additive antiderivation
Citation: Xiuhai Fei, Cuixian Lu, Haifang Zhang. Nonlinear Jordan triple derivable mapping on $ * $-type trivial extension algebras[J]. Electronic Research Archive, 2024, 32(3): 1425-1438. doi: 10.3934/era.2024066

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Abstract

The aim of the paper was to give a description of nonlinear Jordan triple derivable mappings on trivial extension algebras. We proved that every nonlinear Jordan triple derivable mapping on a $ 2 $-torsion free $ * $-type trivial extension algebra is a sum of an additive derivation and an additive antiderivation. As an application, nonlinear Jordan triple derivable mappings on triangular algebras were characterized.

References

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