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

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

$\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解

仝兆佳 胡乃红

仝兆佳, 胡乃红. $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解[J]. 华东师范大学学报(自然科学版), 2012, (3): 71-84,96.
引用本文: 仝兆佳, 胡乃红. $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解[J]. 华东师范大学学报(自然科学版), 2012, (3): 71-84,96.
TONG Zhao-jia, HU Nai-hong. Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 71-84,96.
Citation: TONG Zhao-jia, HU Nai-hong. Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules[J]. Journal of East China Normal University (Natural Sciences), 2012, (3): 71-84,96.

$\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm sl}_{\bf 2}\textbf{)}$\,关于主不可分解模的直和分解

详细信息
  • 中图分类号: O152

Direct sum decomposition of $\overline{\emph{\textbf{U}}}_{{\bm r},{\bm s}}\textbf{(}{\bm s}{\bm l}_{\bf 2}\textbf{)}$ about principal indecomposable modules

  • 摘要: 描述了限制型双参数量子群\,$\overline{U}_{r,s}(sl_2)$\,的一类不可约模, 构造出\,$\overline{U}_{r,s}(sl_2)$\,所有的主不可分解模. 把\,Casimir\,元素的左乘作用看作\,$\overline{U}_{r,s}(sl_2)$\,到自身的线性变换, 得到了\,Casmir\,元素作用在\,$\overline{U}_{r,s}(sl_2)$\,上的极小多项式和\,$\overline{U}_{r,s}(sl_2)$\,本原幂等元的全部共轭类.
  • [1] {1}JANTZEN J C. Lectures on Quantum Groups[M]. Graduate Studies in

    Math 6. Providence: Amer Math Soc, 1996.
    {2}KASSEL C. Quantum Groups[M]. Graduate Text in Mathmatics, 155, New

    York: Springer-Verlag, 1995.
    {3}CONCINI D E, KAC V G. Representations of Quantum Groups at root of 1[C]// CONNES A. Operator Algebras, Unitary Representation,

    Enveloping Algebras, and Invariant Theory(Colloque Dixmier), Proc

    Paris 1989: Progress in Mathmatics 92. 1990: 471-506.
    {4}BERGERON N, GAO Y, HU N. Drinfel'd doubles and Lusztig's symmetric

    of two-parameter quantum groups[J]. J Algebra, 2006, 301: 378-405.
    {5}BENKART G, WITHERSPOON S. Representations of two-parameter quanrum

    groups and Schur-Weyl duality[C]// Hopf algebras: Lecture Notes in

    Pure and Appl Math 237, New York: Dekker. 2004: 62-92.
    {6}HU N, SHI Q. The two-parameter quantum group of exceptional type

    $G_2$ and Lusztig symmetries[J]. Pacific J Math, 2007, 230(2):

    327-346.
    {7}BAI X, HU N. Two-parameter quantum group of exceptional type

    E-series ans conves PBW type basis[J]. Algebra Colloq, 2008, 15(4):

    619-636.
    {8}BENKART G, WITHERSPOON S. Restricted two-parameter quantum groups[C]// Fields Institute Communications. Representations of Finite

    Dimensional Algebras and Related Topics in Lie Theory and Geometry

    Providence: Amer Math Soc, 2004, 40: 293-318.
    {9}HU N, WANG X. Conves PBW-type Lyondon basis and restricted

    two-parameter quantum groups of type B[J]. J Geom Phys, 2010, 60(3):

    430-453.
    {10}HU N, WANG X. Conves PBW-type Lyondon basis and restricted

    two-parameter quantum groups of type $G_2$[J]. Pacific J Math, 2009,

    241(2): 243-273.
    {11}陈茹. 限制的\,$C$\,型双参数量子群[D]. 上海: 华东师范大学, 2008.
    {12}白晓棠. 双参数~$E$~型量子群和限制~$D$~双参数量子群[D].~上海:~华东师范大学,~2006.
    {13}XIAO J. Finite dimensional representationas of

    ~$\overline{U}_{t}(sl_2)$~at root of unity[J].~Can J Math,

    1997,~49:~772-787.
    {14}CHARI V, PREMET A. Indecomposable restricted representations of

    quantum $sl_2$[J].~Publ RIMS Kyoto Univ,~1994,~30:~335-352.
    {15}ARIKE Y. A construction of symmetric linear functions of the

    restricted quantum group $\overline{U}_{q}(sl_2)$[J].~Osaka J

    Math,~2010, 47(2): 535-557.
    {16}ABE E. Hopf Albgebras[M]. Cambridge:~Cambridge University

    Press,~1990.
    {17}德洛兹锝,~基里钦柯,~有限维代数[M].~刘绍学,~张英伯

    译, 北京:~北京师范大学出版社,~1984.
  • 加载中
计量
  • 文章访问数:  4358
  • HTML全文浏览量:  18
  • PDF下载量:  2094
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-09-01
  • 修回日期:  2011-12-01
  • 刊出日期:  2012-05-25

目录

    /

    返回文章
    返回