On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

被引：1

作者：

Duan, Fei Fei ^{[1
]}

Shu, Bin ^{[2
]}

Yao, Yu Feng ^{[3
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Shanghai 200241, Peoples R China

[3] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2020年 / 36卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Lie superalgebra of Cartan type; restricted representation; block; ALGEBRAS;

D O I：

10.1007/s10114-020-9469-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let g be a restricted Lie superalgebra of Cartan typeW(n),S(n)orH(n) over an algebraically closed fieldkof prime characteristicp> 3, in the sense of modular version of Kac's definition in 1977. In this note, we show that the restricted representation category overghas only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.

引用

页码：1061 / 1075

页数：15

共 50 条

[21] Representations of the Restricted Cartan Type Lie Superalgebra W (m, n, 1)
Bin Shu
Chaowen Zhang
Algebras and Representation Theory, 2011, 14 : 463 - 481
[22] Representations for Lie superalgebras of type C
Shader, CL
JOURNAL OF ALGEBRA, 2002, 255 (02) : 405 - 421
[23] Representations of the Restricted Cartan Type Lie Superalgebra W (m, n, 1)
Shu, Bin
Zhang, Chaowen
ALGEBRAS AND REPRESENTATION THEORY, 2011, 14 (03) : 463 - 481
[24] Block Degeneracy for Graded Lie Superalgebras of Cartan Type
Ou, Ke
JOURNAL OF LIE THEORY, 2020, 30 (01) : 145 - 154
[25] Super-biderivations of Cartan type Lie superalgebras
Yuan, Jixia
Chen, Liangyun
Cao, Yan
COMMUNICATIONS IN ALGEBRA, 2021, 49 (10) : 4416 - 4426
[26] Blocks of Lie superalgebras of type W(n)
Shomron, N
JOURNAL OF ALGEBRA, 2002, 251 (02) : 739 - 750
[27] Superderivations for Modular Graded Lie Superalgebras of Cartan-type
Bai, Wei
Liu, Wende
ALGEBRAS AND REPRESENTATION THEORY, 2014, 17 (01) : 69 - 86
[28] Superderivations for Modular Graded Lie Superalgebras of Cartan-type
Wei Bai
Wende Liu
Algebras and Representation Theory, 2014, 17 : 69 - 86
[29] ON GENERALIZED REDUCED REPRESENTATIONS OF RESTRICTED LIE SUPERALGEBRAS IN PRIME CHARACTERISTIC
Yao, Y. F.
Li, Y. Y.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2015, 41 (05): : 1271 - 1285
[30] Simple modules for some Cartan-type Lie superalgebras
Wei, Zhu
Zhang, Yongzheng
Zhang, Qingcheng
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2015, 44 (01): : 129 - 152

← 1 2 3 4 5 →