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

被引：55

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
Benkovic, Dominik
[J]. 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
BRESAR, M
[J]. JOURNAL OF ALGEBRA, 1995, 172 (03) : 764 - 786
[4] Commuting maps: A survey
Bresar, M
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2004, 8 (03): : 361 - 397
[5] CENTRALIZING MAPS IN PRIME-RINGS WITH INVOLUTION
BRESAR, M
MARTINDALE, WS
MIERS, CR
[J]. JOURNAL OF ALGEBRA, 1993, 161 (02) : 342 - 357
[6] BIDERIVATIONS AND LINEAR COMMUTING MAPS ON SIMPLE GENERALIZED WITT ALGEBRAS OVER A FIELD
Chen, Zhengxin
[J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2016, 31 : 1 - 12
[7] On the extended centroid of prime associative superalgebras with applications to superderivations
Fosner, M
[J]. COMMUNICATIONS IN ALGEBRA, 2004, 32 (02) : 689 - 705
[8] UNITARY REPRESENTATIONS OF THE VIRASORO AND SUPER-VIRASORO ALGEBRAS
GODDARD, P
KENT, A
OLIVE, D
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 103 (01) : 105 - 119
[9] LIE SUPER-ALGEBRAS
KAC, VG
[J]. ADVANCES IN MATHEMATICS, 1977, 26 (01) : 8 - 96
[10] Left-symmetric superalgebraic structures on the super-Virasoro algebras
Kong, Xiaoli
Bai, Chengming
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2008, 235 (01) : 43 - 55

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