Higher Jordan triple derivations on $ * $-type trivial extension algebras

Xiuhai Fei; Zhonghua Wang; Cuixian Lu; Haifang Zhang; Xiuhai Fei; Zhonghua Wang; Cuixian Lu; Haifang Zhang

doi:10.3934/math.2024338

AIMS Mathematics

2024, Volume 9, Issue 3: 6933-6950. doi: 10.3934/math.2024338

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Research article

Higher Jordan triple derivations on $ * $-type trivial extension algebras

1.
School of Mathematics and Physics, West Yunnan University, Lincang, China
2.
School of Science, Xi'an Shiyou University, Xi'an, China
3.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an, China

Received: 15 November 2023 Revised: 27 January 2024 Accepted: 04 February 2024 Published: 19 February 2024
MSC : 16W25, 46L10

In this paper, we investigated the problem of describing the form of higher Jordan triple derivations on trivial extension algebras. We show that every higher Jordan triple derivation on a $ 2 $-torsion free $ * $-type trivial extension algebra is a sum of a higher derivation and a higher anti-derivation. As for its applications, higher Jordan triple derivations on triangular algebras are characterized.
- derivation,
- anti-derivation,
- higher derivation,
- higher anti-derivation,
- higher Jordan triple derivation
Citation: Xiuhai Fei, Zhonghua Wang, Cuixian Lu, Haifang Zhang. Higher Jordan triple derivations on $ * $-type trivial extension algebras[J]. AIMS Mathematics, 2024, 9(3): 6933-6950. doi: 10.3934/math.2024338

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Abstract

In this paper, we investigated the problem of describing the form of higher Jordan triple derivations on trivial extension algebras. We show that every higher Jordan triple derivation on a $ 2 $-torsion free $ * $-type trivial extension algebra is a sum of a higher derivation and a higher anti-derivation. As for its applications, higher Jordan triple derivations on triangular algebras are characterized.

References

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