Representations of Lie conformal algebras related to Galilean conformal algebras

被引：1
|
作者：
Han, Xiu [1 ,2 ]
Wang, Dengyin [1 ]
Xia, Chunguang [1 ]
机构：
[1] China Univ Min & Technol, Sch Math, Xuzhou 221116, Jiangsu, Peoples R China
[2] Xuzhou Univ Technol, Sch Math & Phys, Xuzhou, Jiangsu, Peoples R China
来源：
COMMUNICATIONS IN ALGEBRA | 2022年 / 50卷 / 06期
关键词：
Conformal module; extension problem; Galilean conformal algebra; Lie conformal algebra; COHOMOLOGY;
D O I：
10.1080/00927872.2021.2007393
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the representation theory of Lie conformal analogues r(a, b) of certain Galilean conformal algebras, where a, b are complex numbers. We first classify their finite irreducible conformal modules, and then solve the extension problem. In particular, we obtain several classes of new indecomposable conformal modules over r(a, b).
引用
收藏
页码：2427 / 2438
页数：12
相关论文
共 50 条
  • [31] Multi-graded Galilean conformal algebras
    Ragoucy, Eric
    Rasmussen, Jorgen
    Raymond, Christopher
    NUCLEAR PHYSICS B, 2020, 957
  • [32] CONFORMAL DERIVATIONS OF SEMIDIRECT PRODUCTS OF LIE CONFORMAL ALGEBRAS AND THEIR CONFORMAL MODULES
    Guo, Jiancang
    Tan, Youjun
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (05) : 1471 - 1483
  • [33] Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras
    Su, Yucai
    Yue, Xiaoqing
    JOURNAL OF ALGEBRA, 2021, 588 : 408 - 424
  • [34] Extending Structures for Lie Conformal Algebras
    Yanyong Hong
    Yucai Su
    Algebras and Representation Theory, 2017, 20 : 209 - 230
  • [35] Extending Structures for Lie Conformal Algebras
    Hong, Yanyong
    Su, Yucai
    ALGEBRAS AND REPRESENTATION THEORY, 2017, 20 (01) : 209 - 230
  • [36] Simplicity of quadratic Lie conformal algebras
    Hong, Yanyong
    Wu, Zhixiang
    COMMUNICATIONS IN ALGEBRA, 2017, 45 (01) : 141 - 150
  • [37] Steinberg unitary Lie conformal algebras
    Mikhalev A.V.
    Pinchuk I.A.
    Journal of Mathematical Sciences, 2007, 142 (2) : 1954 - 1968
  • [38] Finite growth representations of conformal Lie algebras that contain a Virasoro subalgebra
    Boyallian, Carina
    Meinardi, Vanesa
    JOURNAL OF ALGEBRA, 2013, 388 : 141 - 159
  • [39] Conformal Triple Derivations and Triple Homomorphisms of Lie Conformal Algebras
    Asif, Sania
    Luo, Lipeng
    Hong, Yanyong
    Wu, Zhixiang
    ALGEBRA COLLOQUIUM, 2023, 30 (02) : 263 - 280
  • [40] Central extensions and conformal derivations of a class of Lie conformal algebras
    Hong, Yanyong
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (18): : 3577 - 3598
12345