Characterizations of Lie derivations of triangular algebras

被引:88
作者
Ji, Peisheng [1 ]
Qi, Weiqing [2 ]
机构
[1] Qingdao Univ, Coll Math, Qingdao 266071, Peoples R China
[2] Qingdao Univ, Coll Informat Engn, Qingdao 266071, Peoples R China
基金
中国国家自然科学基金;
关键词
Lie derivation; Derivation; Triangular algebra; ALL-DERIVABLE POINTS; CHARACTERIZING HOMOMORPHISMS; OPERATOR;
D O I
10.1016/j.laa.2011.02.048
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T, we prove that if delta : T -> T is an R-linear map satisfying delta([x, y]) = [delta(x), y] + [x, delta(y)] for any x, y is an element of T with xy = 0 (resp. xy = p, where p is the standard idempotent of T), then delta = d + tau, where d is a derivation of T and tau : T -> Z(T) (where Z(T) is the center of T) is an R-linear map vanishing at commutators [x. y] with xy = 0 (resp. xy = P). Lie derivation (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码:1137 / 1146
页数:10
相关论文
共 18 条
[1]  
Alaminos J, 2007, P ROY SOC EDINB A, V137, P1
[2]   Symmetric amenability and Lie derivations [J].
Alaminos, J ;
Mathieu, M ;
Villena, AR .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2004, 137 :433-439
[3]   Characterizations of derivations on triangular rings: Additive maps derivable at idempotents [J].
An, Runling ;
Hou, Jinchuan .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (5-7) :1070-1080
[4]  
Bresar M, 2007, P ROY SOC EDINB A, V137, P9
[5]   Maps characterized by action on zero products [J].
Chebotar, MA ;
Ke, WF ;
Lee, PH .
PACIFIC JOURNAL OF MATHEMATICS, 2004, 216 (02) :217-228
[6]   Lie derivations of triangular algebras [J].
Cheung, WS .
LINEAR & MULTILINEAR ALGEBRA, 2003, 51 (03) :299-310
[7]   Commuting maps of triangular algebras [J].
Cheung, WS .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2001, 63 :117-127
[8]   DERIVATIONS OF NEST ALGEBRAS [J].
CHRISTENSEN, E .
MATHEMATISCHE ANNALEN, 1977, 229 (02) :155-161
[9]  
Davision K.R., 1980, NEST ALGEBRAS PITMAN, V191
[10]   Additive maps derivable at some points on J-subspace lattice algebras [J].
Hou, Jinchuan ;
Qi, Xiaofei .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 429 (8-9) :1851-1863