三角代数上的Jordan双导子  

Jordan Biderivations on Triangular Algebras

作　　者：任丹丹 梁新峰 REN Dandan;LIANG Xinfeng(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan,Anhui,232001,P.R.China)

机构地区：[1]安徽理工大学数学与大数据学院,淮南安徽232001

出　　处：《数学进展》2022年第2期299-312,共14页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11801008);Key Projects of Natural Science Foundation of Anhui Education Department(Nos.KJ2018A0082,KJ2019A0107);Natural Science Foundation of Anhui Province(No.2008085QA01);Key Program of Scientific Research Fund for Young Teachers of AUST(No.QN2017209)。

摘　　要：设T是定义在交换环上R的三角代数,φ:T×T→T是定义在T上的任意Jordan双导子.受[Comm.Algebra,2017,45(4):1741--1756]和[Linear Algebra Appl.,2009,431(9):1587--1602]研究的启发,本文致力研究φ的结构形式.我们指出在适当条件下Jordan双导子φ可以分解成内双导子和extremal双导子之和,推广了本方向现有成果.本文结果可直接应用于分块上三角矩阵代数和Hilbert空间定义的套代数.Let T be a triangular algebra over a commutative ring R andφ:T×T→T be an arbitrary Jordan biderivation of T.Motivated by the elegant and powerful works of[Comm.Algebra,2017,45(4):1741-1756]and[Linear Algebra Appl.,2009,431(9):1587-1602],we will address the question of describing the form ofφin the current work.It is shown that under certain mild assumptions,φis the sum of an inner biderivation and an extremal biderivation,which explicitly extends the existing works in this vein.Our results are immediately applied to block upper triangular algebras and Hilbert space nest algebras.

关 键 词：Jordan双导子 双导子 三角代数 

分 类 号：O153.3[理学—数学]