Lie derivations of incidence algebras

被引：23

作者：

Zhang, Xian ^{[1
]}

Khrypchenko, Mykola ^{[2
]}

机构：

[1] Huaqiao Univ, Sch Math Sci, Quanzhou 362021, Fujian, Peoples R China

[2] Univ Fed Santa Catarina, Dept Matemat, Campus Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, SC, Brazil

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2017年 / 513卷

关键词：

Derivation; Lie derivation; Incidence algebra; FINITARY INCIDENCE RINGS; TRIANGULAR ALGEBRAS; JORDAN DERIVATIONS; AUTOMORPHISMS; INVOLUTIONS;

D O I：

10.1016/j.laa.2016.10.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a locally finite preordered set, R a commutative ring with identity and I(X, R) the incidence algebra of X over R. In this note we prove that each Lie derivation of I(X, R.) is proper, provided that R is 2-torsion free. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：69 / 83

页数：15

共 24 条

[1]

[Anonymous], 1997, Enumerative combinatorics

[2] Lie derivations on triangular matrices [J].

Benkovic, Dominik .

LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (06) :619-626

[3] Generalized Lie derivations on triangular algebras [J].

Benkovic, Dominik .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 434 (06) :1532-1544

[4] Commuting maps: A survey [J].

Bresar, M .

TAIWANESE JOURNAL OF MATHEMATICS, 2004, 8 (03) :361-397

[5] COMMUTING TRACES OF BIADDITIVE MAPPINGS, COMMUTATIVITY-PRESERVING MAPPINGS AND LIE MAPPINGS [J].

BRESAR, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 335 (02) :525-546

[6] Classification of involutions on finitary incidence algebras [J].

Brusamarello, Rosali ;

Fornaroli, Erica Zancanella ;

Santulo Junior, Ednei Aparecido .

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2014, 24 (08) :1085-1098

[7] Automorphisms and involutions on incidence algebras [J].

Brusamarello, Rosali ;

Lewis, David W. .

LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (11) :1247-1267

[8] Lie derivations of triangular algebras [J].

Cheung, WS .

LINEAR & MULTILINEAR ALGEBRA, 2003, 51 (03) :299-310

[9] Lie derivations of generalized matrix algebras [J].

Du, Yiqiu ;

Wang, Yu .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 437 (11) :2719-2726

[10] LIE AND JORDAN STRUCTURES IN SIMPLE, ASSOCIATIVE RINGS [J].

HERSTEIN, IN .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1961, 67 (06) :517-&

← 1 2 3 →