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弱Hopf代数上的β-特征代数 被引量：1

β-Character Algebras Over Weak Hopf Algebras
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摘要 考虑了弱Hopf代数上的β-特征代数.当H是有限维弱Hopf代数时,给出了g∈Cβ(H)(Cβ(H)是H*的β-特征)的一个充要条件,并研究了弱Hopf代数上的β-广义特征代数. The paper is concerned with the β-character algebras in the case of weak Hopf algebras. We present a sufficient and necessary condition that any elementg∈H^＋ is in the β-character algebra Cβ （H） , where H is a finite dimeninal weak Hopf algebra. Furthermore, we investigate the β-generalized character algebras over weak Hopf algebras.
作者 李彦超 王勇 张良云
机构地区 南京农业大学理学院
出处 《南京师大学报（自然科学版）》 CAS CSCD 北大核心 2009年第4期36-41,共6页 Journal of Nanjing Normal University(Natural Science Edition)
基金 国家自然科学基金(10871170) 教育部科学技术重点研究(108154)资助项目
关键词 弱HOPF代数 β-特征代数 群像元素 weak Hopf algebra,β-character algebra, group-like element
分类号 O153.3 [理学—基础数学]
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参考文献13

  • 1Bohm G, Nill F, Szlachanyi K. Weak Hopf algebras I. Integral theory and C^* -structure [ J ]. Journal of Algebra, 1999, 221 : 385-438.
  • 2Hayashi T. Quantum group symmetry of partition functions of IRF models and its applications to Jones's index theory [ J ]. Communications in Mathematical Physics, 1993, 157: 331-345.
  • 3Nikshych D, Vainermun L. Finite quantum groupoids and their applications [ J]. Mathematical Sciences Research Institute Publications, 2002, 43:211-262.
  • 4Yamanouchi T. Duality for generalized Kac algebras and a characterization of finite groupoid algebras [ J ]. Journal of Algebra, 1994, 163: 9-50.
  • 5Nikshyeh D. A duality theorem for quantum groupoids[ J]. Contemporary Mathematics, 2000, 267: 237-243.
  • 6Zhang L Y, Zhu S L. Fundamental theorems of weak Doi-Hopf modules and semisimple weak smash product Hopf algebras [ J ]. Communications in Algebra, 2004, 32 (9) : 3 403-3 415.
  • 7Doi Y. On the structure of relative Hopf modules[ J]. Communications in Algebra, 1983, 11 (3) : 243-255.
  • 8张良云.弱Hopf代数上的Maschke定理和Morita关系[J].中国科学（A辑）,2006,36(2):192-203. 被引量：9
  • 9Cohen M, Fishman D. Hopf algebra actions[J]. Journal of Algebra, 1986, 100:363-379.
  • 10Hu J, Zhang Y H. The β-character algebras and a commuting pair in Hopf algebras[ J]. Algebra Representation Theory, 2007, 10: 497-516.

二级参考文献14

  • 1Bohm G,Nill F,Szlachányi K.Weak Hopf algebras I.Integral theory and C^*-structure.J Algebra,1999,221:385～438
  • 2Hayashi T.Quantum group symmetry of partition functions of IRF models and its applications to Jones's index theory.Comm Math Phys,1993,157:331～345
  • 3Nikshych D,Vainerman L.Finite quantum groupoid and their applications.Math Sci Res Inst Publ,2002,43:211～262
  • 4Yamanouchi T.Duality for generalized Kac algebras and a characterization of finite groupoid algebras.J Algebra,1994,163:9～50
  • 5Nikshych D.A duality theorem for quantum groupoids.Contemp Math,2000,267:237～243
  • 6Zhang L Y,Zhu S L.Fundamental Theorems of weak Doi-Hopf modules and semisimple weak smash product Hopf algebras.Comm Algebra,2004,32(9):3403～3415
  • 7Doi Y.On the structure of relative Hopf modules.Comm Algebra,1983,11(3):243～255
  • 8Cohen M,Fishman D.Hopf algebra actions.J Algebra,1986,100:363～379
  • 9Montgomery S.Hopf Algebras and Their Actions on Rings.Regional Conference Series in Mathematics,No 82.Providence:Amer Math Soc,1993
  • 10Zhang L Y,Chen H X,Li J Q.Twisted products and smash products over weak Hopf algebras.Acta Math Scientia (Series B),2004,24(2):247～258

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南京师大学报（自然科学版）
2009年 第4期

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