Biderivations And Linear Commuting Maps on the Schrodinger-Virasoro Lie Algebra

被引：79

作者：

Wang, Dengyin ^{[1
]}

Yu, Xiaoxiang ^{[2
]}

机构：

[1] China Univ Min & Technol, Coll Sci, Xuzhou 221116, Peoples R China

[2] Xuzhou Normal Univ, Sch Math & Comp Sci, Xuzhou, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2013年 / 41卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Biderivations; Commuting maps; Schrodinger-Virasoro Lie algebra; 17B05; 17B20; 17B30; 17B40;

D O I：

10.1080/00927872.2012.654551

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let ? be the Schrdinger-Virasoro Lie algebra over the complex field C. In this article, we prove that each biderivation of ? is inner. As an application of biderivations, we show that every linear commuting map on ? has the form (x)=x+f(x)M-0, where C, M-0 is a basis of the one-dimensional center of ?, and f is a linear function from ? to C.

引用

页码：2166 / 2173

页数：8

共 12 条

[1] Biderivations of triangular algebras [J].

Benkovic, Dominik .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 431 (09) :1587-1602

[2] ON GENERALIZED BIDERIVATIONS AND RELATED MAPS [J].

BRESAR, M .

JOURNAL OF ALGEBRA, 1995, 172 (03) :764-786

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

Bresar, M .

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

[4] CENTRALIZING MAPS IN PRIME-RINGS WITH INVOLUTION [J].

BRESAR, M ;

MARTINDALE, WS ;

MIERS, CR .

JOURNAL OF ALGEBRA, 1993, 161 (02) :342-357

[5] Lie bialgebra structures on the Schrodinger-Virasoro Lie algebra [J].

Han, Jianzhi ;

Li, Junbo ;

Su, Yucai .

JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (08)

[6] SCHRODINGER INVARIANCE AND STRONGLY ANISOTROPIC CRITICAL SYSTEMS [J].

HENKEL, M .

JOURNAL OF STATISTICAL PHYSICS, 1994, 75 (5-6) :1023-1061

[7]

LI JB, 2008, ARXIV08012207V1

[8] Representations of the Schrodinger-Virasoro algebras [J].

Li, Junbo ;

Su, Yucai .

JOURNAL OF MATHEMATICAL PHYSICS, 2008, 49 (05)

[9] 2-cocycles of original deformative Schrodinger-Virasoro algebras [J].

Li JunBo ;

Su YuCai ;

Zhu LinSheng .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (11) :1989-1999

[10] On vertex algebra representations of the Schrodinger-Virasoro Lie algebra [J].

Unterberger, Jeremie .

NUCLEAR PHYSICS B, 2009, 823 (03) :320-371

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