Jordan代数上的可乘Jordan导子

纪培胜, 赖弋新, 侯恩冉

数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 571-578.

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数学学报 ›› 2010, Vol. 53 ›› Issue (3) : 571-578. DOI: 10.12386/A2010sxxb0063
论文

Jordan代数上的可乘Jordan导子

    纪培胜, 赖弋新, 侯恩冉
作者信息 +

Multiplicative Jordan Derivations on Jordan Algebras

    Pei Sheng JI, Yi Xin LAI, En Ran HOU
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文章历史 +

摘要

A是Jordan代数, 如果映射d:AA满足任给a,bA,都有 d(a o b)=d(a) o b+a o d(b), 则称d为可乘Jordan导子. 如果A含有一个非平凡幂等p,且A对于p的Peirce分解 A=A1A1/2A0满足:
(1) 设aiAi (i=1,0),如果任给t1/2A1/2,都有ai o t1/2=0,则ai=0,则A上的可乘Jordan导子d. 如果满足d(p)=0,则d是可加的.由此得到结合代数和三角代数满足一定条件时,其上的任意可乘Jordan导子是可加的.

 

Abstract

Let A be a Jordan algebra. If the map d:AA satisfies d(a o b)=d(a) o b+a o d(b) for all a,bA, then d is called a multiplicative Jordan derivation on A. Our main objective in this note is to prove the following. Suppose A has an idempotent p (p≠0,p≠1) which satisfies that the Peirce decomposition of A with respect to p, A=A1A1/2A0, satisfies that
(1) Let aiAi (i=1,0). If ai o t1/2=0 for all t1/2A1/2, then ai=0. If d is any multiplicative Jordan derivation of A which satisfies that d(p)=0, then d is additive. As its application, we get the result that every multiplicative Jordan derivation on some associative algebras and triangular algerbas is additive.

 

关键词

Jordan代数 / 可乘Jordan导子 / 可加性

Key words

Jordan algebra / multiplicative Jordan derivation / additivity

引用本文

导出引用
纪培胜, 赖弋新, 侯恩冉. Jordan代数上的可乘Jordan导子. 数学学报, 2010, 53(3): 571-578 https://doi.org/10.12386/A2010sxxb0063
Pei Sheng JI, Yi Xin LAI, En Ran HOU. Multiplicative Jordan Derivations on Jordan Algebras. Acta Mathematica Sinica, Chinese Series, 2010, 53(3): 571-578 https://doi.org/10.12386/A2010sxxb0063

参考文献


[1] Martindale W. S., When are multiplicative mappings additive, Proc. Amer. Math. Soc., 1969, 21: 695--698.

[2] Daif M. N., When is a multiplicative derivation additive, Internat J. Math. and Math. Sci., 1991, 14: 615--618.

[3] Du W., Zhang J. H., Multiplicative derivations on nest algebras, Basic Science J. of Textile Univ., 2007, 20(2): 153--155 (in Chinese).

[4] Ji P. S., Qi W. Q., Multiplicative derivations on triangular algebras, J. Guangxi Normal Univ., 2008, 26(3): 26--28 (in Chinese).

[5] Wu J., Lu S. J., Generalized Jordan derivations on prime rings and standard operator algebras, Taiwanese J. Math., 2003, 7(4): 605--613.

[6] Dominik B., Jordan derivations and antiderivations on triangular matrices, Linear Algebra and its Applications, 2005, 397: 235--244.

[7] Hanche-Olsen H., Stormer E., Jordan Operator Algebras, London: Pitman Press, 1984.

[8] Cheung W. S., Mappings on Triangular Algebras, PhD Dissertation, U. Vic., 2000.

基金

国家自然科学基金资助项目(10971117,10675086); 山东省基金资助项目(Y2006A04)

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