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双边群Smash余积的半单性 被引量：1

Semisimplicity of Two-Sided Group Smash Coproducts
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摘要 通过引入双边群Smash余积的概念,给出了双边群Smash余积成为Hopf群余代数的充要条件,并利用群余代数中积分理论讨论了双边群Smash余积的半单性. By introducing the concept of two-sided group Smash coproducts,the authors presented the necessary and sufficient conditions for two-sided group Smash coproducts to be Hopf group coalgebras.Using the integral theories of Hopf group coalgebras,we discussed the semisimphcity of two-sided group Smash coproducts.
作者 李德胜 陈全国 王顶国
机构地区 鲁东大学数学与信息学院 伊犁师范学院数学与统计学院 曲阜师范大学数学科学学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2013年第3期431-433,共3页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11261063 11171183) 山东省自然科学基金(批准号:ZR2011AM013) 新疆维吾尔自治区普通高校重点学科研究项目(批准号:2012ZDXK03)
关键词 HOPF群余代数 余模余代数 半单性 Hopf group coalgebras comodule coalgebras semisimplicity
分类号 O153.3 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Virelizier A. Hopf Group-Coalgebras[J].Journal of Pureand Applied Algebra, 2002, 171(1): 75-122.
  • 2Zunino M. Double Construction for Crossed Hopf Coalgebra[J].Journal of Algebra, 2004, 278(1):.43-7.5.
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  • 4WANG Shuan-hong. Group Entwining Structures and Group Coalgebra Galois Extensions[J]. Comm Algebra, 2004, 32(9): 3437-3457.
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  • 6WANG Shuan-hong. Morita Contexts, rr-Galois Extensions for Hopf zr-Coalgebras[J]. Comm Algebra, 2006, 34(2): 521-546.
  • 7Montgomery S. Hopf Algebras and Their Actions on Rings[MJ. Providence: American Mathematical Society, 1993.
  • 8陈全国,汤建钢.弱π-缠绕模的Maschke型定理[J].吉林大学学报（理学版）,2012,50(4):603-606. 被引量：2

二级参考文献10

  • 1WANG Shuan-hong. Group Entwining Structures and Group Coalgebra Galois Extensions [ J 1. Comm Algebra, 2004, 32 (9) : 3437-3457.
  • 2JIA Ling, LI Fang. On Weak Group Entwined Structure [ J ]. Houston Journal of Mathematics, 2007,33 (2) : 433-450.
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  • 6WANG Shuan-hong. A Maschke-Type Theorem for Hopf 7r-Comodules [J]. Tsukuba J Math, 2004, 28(2) : 377-388.
  • 7陈全国,汤建钢.弱Hopf群n余代数上的弱Doi-Hoof群模[J].数学学报:中文版,2011,54(4):697-704.
  • 8Daele A, Van, WANG Shuan-hong. New Braided Crossed Categories and Drinfeld Quantum Double for Weak Hopf-Coalgebras [ J ]. Comm Algebra, 2008, 36 (6) : 2341-2386.
  • 9LIU Ling, WANG Shuan-hong. Constructing New Braided T-Categories over Weak Hopf Algebras [ J ]. Appl Categor Struet, 2010, 18(4) : 431-459.
  • 10ZHU Hai-xing, WANG Shuan-hong. A Generalized Drinfeld Quantum Double Construction Based on Weak Hopf Algebras [ J ]. Comm Algebra, 2010, 38 ( 1 ) : 199-229.

共引文献1

同被引文献11

  • 1Turaev V G. Homopology Quantum Field Theorey [M]. Zurieh: Eur Math Soe, 2010.
  • 2WANG Shuanhong. Coquasitriangular Hopf Group Algebras and Drinfel' d Co-doubles [J]. Comm Algebra, 2007, 35(1): 77-101.
  • 3MA Tianshui, WANG Shuanhong. General Double Quantum Groups [J]. Comm Algebra, 2010, 38(2): 645-672.
  • 4CHEN Quanguo. The Quasitriangular Structures for a Class of Group Twisted Product Hopf Group Coalgebras [J]. J Algebra Appl, 2015, 14(4), 1550049.
  • 5TANG Juan, CHEN Quanguo, FANG Yong. Group Unified Coprodcuts and Related Quasitriangular Structures [J]. Filomat, 2015, 29(8) : 1729-1751.
  • 6Virelizier A. Hopf Group-Coalgebras [J], J Pure Appl Algebra, 2002, 171(1): 75-122.
  • 7Zunino M. Double Construction for Crossed Hopf Coalgebras [J]. J Algebra, 2004, 278(1): 43-75.
  • 8WANG Dingguo, LU Daowei. OreLExtensions of Hopf Group Coalgebras [J]. J Korean Math Soc, 2014, 51 (2) 325-344.
  • 9WANG Dingguo, CHEN Quanguo. A Maschke Type Theorem for Weak Group Entwined Modules and Applications [J]. Israel J Math, 2014, 204(1) : 329-358.
  • 10CHEN Quanguo, WANG Dingguo. A Class of Coquasitriangular Hopf Group Algebras [J]. Comm Algebra, 2016, 44(1): 310-335.

引证文献1

吉林大学学报（理学版）
2013年 第3期

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