Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras

Ai-qun Ma; Lin Chen; Zijie Qin; Ai-qun Ma; Lin Chen; Zijie Qin

doi:10.3934/math.2023304

AIMS Mathematics

2023, Volume 8, Issue 3: 6026-6035. doi: 10.3934/math.2023304

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Research article

Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras

1.
Department of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
2.
Department of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, China

Received: 05 August 2022 Revised: 11 December 2022 Accepted: 12 December 2022 Published: 29 December 2022
MSC : 46K15, 47B49

In this paper, we investigate Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras over the field of real numbers. We prove that every Jordan semi-triple derivation on generalized quaternion algebras over the field of real numbers is a derivation. Also, we show that every left (resp, right) Jordan centralizer on generalized quaternion algebras over the field of real numbers is a left (resp, right) centralizer.
- generalized quaternion algebra,
- Jordan semi-triple derivation,
- Jordan centralizer
Citation: Ai-qun Ma, Lin Chen, Zijie Qin. Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras[J]. AIMS Mathematics, 2023, 8(3): 6026-6035. doi: 10.3934/math.2023304

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Abstract

In this paper, we investigate Jordan semi-triple derivations and Jordan centralizers on generalized quaternion algebras over the field of real numbers. We prove that every Jordan semi-triple derivation on generalized quaternion algebras over the field of real numbers is a derivation. Also, we show that every left (resp, right) Jordan centralizer on generalized quaternion algebras over the field of real numbers is a left (resp, right) centralizer.

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