Linear Super-Commuting Maps and Super-Biderivations on the Super-Virasoro Algebras

被引：56

作者：

Xia, Chunguang ^{[1
]}

Wang, Dengyin ^{[1
]}

Han, Xiu ^{[2
]}

机构：

[1] China Univ Min & Technol, Dept Math, Xuzhou 221116, Jiangsu, Peoples R China

[2] Xuzhou Inst Technol, Sch Math & Phys Sci, Xuzhou, Jiangsu, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2016年 / 44卷 / 12期

关键词：

Super-biderivations; Super-commuting maps; Super-Virasoro algebras;

D O I：

10.1080/00927872.2016.1172617

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let SVir be the well-known super-Virasoro algebras. In this paper, we first prove that any super-skewsymmetric super-biderivation of SVir is inner. Based on this, we show that every linear super-commuting map on SVir is of the form (x)=f(x)c, where f is a linear function from SVir to C mapping the odd part of SVir to zero, and c is the central charge of SVir.

引用

页码：5342 / 5350

页数：9

共 16 条

[1] Biderivations of triangular algebras [J].

Benkovic, Dominik .

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

[2]

Brear M., 1991, P AM MATH SOC, V111, P501

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

BRESAR, M .

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

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

Bresar, M .

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

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

BRESAR, M ;

MARTINDALE, WS ;

MIERS, CR .

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

[6] BIDERIVATIONS AND LINEAR COMMUTING MAPS ON SIMPLE GENERALIZED WITT ALGEBRAS OVER A FIELD [J].

Chen, Zhengxin .

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 :1-12

[7] On the extended centroid of prime associative superalgebras with applications to superderivations [J].

Fosner, M .

COMMUNICATIONS IN ALGEBRA, 2004, 32 (02) :689-705

[8] UNITARY REPRESENTATIONS OF THE VIRASORO AND SUPER-VIRASORO ALGEBRAS [J].

GODDARD, P ;

KENT, A ;

OLIVE, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 103 (01) :105-119

[9] LIE SUPER-ALGEBRAS [J].

KAC, VG .

ADVANCES IN MATHEMATICS, 1977, 26 (01) :8-96

[10] Left-symmetric superalgebraic structures on the super-Virasoro algebras [J].

Kong, Xiaoli ;

Bai, Chengming .

PACIFIC JOURNAL OF MATHEMATICS, 2008, 235 (01) :43-55

← 1 2 →