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
收藏
页码：1061 / 1075
页数：15
相关论文
共 50 条
  • [31] Representations of affine Lie superalgebras and their quantization in type A
    Bezerra, Luan
    Calixto, Lucas
    Futorny, Vyacheslav
    Kashuba, Iryna
    JOURNAL OF ALGEBRA, 2022, 611 : 320 - 340
  • [32] Inverses of Cartan matrices of Lie algebras and Lie superalgebras
    Leites, Dimitry
    Lozhechnyk, Oleksandr
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 583 : 195 - 256
  • [33] Inverses of Cartan matrices of Lie algebras and Lie superalgebras
    Wei, Yangjiang
    Zou, Yi Ming
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 521 : 283 - 298
  • [34] Restricted Cohomology of Restricted Lie Superalgebras
    Ji Xia YUAN
    Liang Yun CHEN
    Yan CAO
    Acta Mathematica Sinica,English Series, 2022, (11) : 2115 - 2130
  • [35] Restricted Cohomology of Restricted Lie Superalgebras
    Yuan, Ji Xia
    Chen, Liang Yun
    Cao, Yan
    ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2022, 38 (11) : 2115 - 2130
  • [36] Restricted Cohomology of Restricted Lie Superalgebras
    Ji Xia Yuan
    Liang Yun Chen
    Yan Cao
    Acta Mathematica Sinica, English Series, 2022, 38 : 2115 - 2130
  • [37] REPRESENTATIONS OF LIE-SUPERALGEBRAS .2. UNITARY REPRESENTATIONS OF LIE-SUPERALGEBRAS OF TYPE-A(N, 0)
    FURUTSU, H
    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY, 1989, 29 (04): : 671 - 687
  • [38] On simple modules for the restricted Lie algebras of cartan type
    Zhang, CW
    COMMUNICATIONS IN ALGEBRA, 2002, 30 (11) : 5393 - 5429
  • [39] MAXIMAL SUBALGEBRAS FOR MODULAR GRADED LIE SUPERALGEBRAS OF ODD CARTAN TYPE
    Liu, Wende
    Wang, Qi
    TRANSFORMATION GROUPS, 2015, 20 (04) : 1075 - 1106
  • [40] Automorphism groups of modular graded Lie superalgebras of Cartan- type
    Liu, Wende
    Yuan, Jixia
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (03)
12345