中国综合性科技类核心期刊(北大核心)

中国科学引文数据库来源期刊(CSCD)

美国《化学文摘》(CA)收录

美国《数学评论》(MR)收录

俄罗斯《文摘杂志》收录

Message Board

Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review, editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!

Name
E-mail
Phone
Title
Content
Verification Code
Issue 3
May  2021
Turn off MathJax
Article Contents
BAI Ruipu, MA Yue. Modules and induced modules of 3-Lie algebra Aω δ[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 8-16. doi: 10.3969/j.issn.1000-5641.2021.03.002
Citation: BAI Ruipu, MA Yue. Modules and induced modules of 3-Lie algebra Aω δ[J]. Journal of East China Normal University (Natural Sciences), 2021, (3): 8-16. doi: 10.3969/j.issn.1000-5641.2021.03.002

Modules and induced modules of 3-Lie algebra Aω δ

doi: 10.3969/j.issn.1000-5641.2021.03.002
  • Received Date: 2020-02-18
  • Publish Date: 2021-05-01
  • For the infinite dimensional simple 3-Lie algebra $A_{\omega}^{\delta}$ over a field $\mathbb F$ of characteristic zero, we construct two infinite dimensional intermediate series modules $(V, \rho_{\lambda, 0})=T_{\lambda, 0}$ and $(V, \rho_{\lambda, 1})=T_{\lambda, 1}$ of $A_{\omega}^{\delta}$ as well as a class of infinite dimensional modules $(V, \psi_{\lambda,\mu})$ of ad$(A_{\omega}^{\delta})$, where $\lambda, \mu\in \mathbb F$. The relation between 3-Lie algebra $A_{\omega}^{\delta}$-modules and induced modules of ad$(A_{\omega}^{\delta})$ are discussed. It is shown that only two of infinite dimensional modules, namely $(V, \psi_{\lambda, 1})$ and $(V, \psi_{\lambda, 0})$, are induced modules.
  • loading
  • [1]
    FILIPPOV V. n-Lie algebras [J]. Siberian Mathematical Journal, 1985, 26(6): 126-140.
    [2]
    BAI R P, WU Y. Constructions of 3-Lie algebras [J]. Linear Multilinear Algebra, 2015, 63(11): 2171-2186. doi:  10.1080/03081087.2014.986121
    [3]
    AZCARRAGA J A, IZQUIERDO J M. n-ary algebras: A review with applications [J]. Journal of Physics A: Mathematical and Theoretical, 2010, 43(29): 293001.
    [4]
    SHENG Y, TANG R. Symplectic, product and complex structures on 3-Lie algebras [J]. Journal of Algebra, 2018, 508: 256-300. doi:  10.1016/j.jalgebra.2018.05.005
    [5]
    BAGGER J, LAMBERT N. Gauge symmetry and supersymmetry of multiple M2-branes [J]. Physical Review D: Particles Fields, 2008, 77(6): 215-240.
    [6]
    DEBELLIS J, SAEMANN C, SZABO R J. Quantized Nambu-Poisson manifolds and n-Lie algebras [J]. Journal of Mathematical Physics, 2010, 51(12): 153-306.
    [7]
    GUATAVSSON A. Algebraic structures on parallel M2 branes [J]. Nuclear Physics B, 2009, 811(1/2): 66-76. doi:  10.1016/j.nuclphysb.2008.11.014
    [8]
    NAMBU Y. Generalized Hamiltonian Dynamics [J]. Physical Review D: Particles Fields, 1999, 7(8): 2405-2412.
    [9]
    TAKHTAJAN L. On foundation of the generalized Nambu mechanics [J]. Communications in Mathematical Physics, 1994, 160(2): 295-315. doi:  10.1007/BF02103278
    [10]
    GAUTHERON P. Some remarks concerning Nambu mechanics [J]. Letters in Mathematical Physics, 1996, 37(1): 103-116. doi:  10.1007/BF00400143
    [11]
    BAI R P, BAI C M, WANG J X. Realizations of 3-Lie algebras [J]. Journal of Mathematical Physics, 2010, 51(6): 063505. doi:  10.1063/1.3436555
    [12]
    BAI R, LI Z H, WANG W D. Infinite-dimensional 3-Lie algebras and their connections to Harish-Chandra modules [J]. Frontiers of Mathematics in China, 2017, 12(3): 515-530. doi:  10.1007/s11464-017-0606-7
    [13]
    KASYMOV S M. Theory of n-Lie algebras [J]. Algebra and Logic, 1987, 26(3): 155-166. doi:  10.1007/BF02009328
    [14]
    LIU J, MAKHLOUF A, SHENG Y. A new approach to representations of 3-Lie algebras and abelian extensions [J]. Algebra Representation Theory, 2017, 20: 1415-1431. doi:  10.1007/s10468-017-9693-0
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views (87) PDF downloads(7) Cited by()
    Proportional views

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return