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构造群缠绕模范畴成为辫子张量范畴 被引量：1

Making the Category of Group Entwined Modules into a Bradied Monoidal Category
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摘要 该文研究了群缠绕模范畴怎样构造成张量范畴,给出的充分条件是要求群缠绕模中的代数和群余代数分别是双代数和半-Hopf群余代数,并满足一些相容条件.作者在张量群缠绕模范畴上构造了辫子.该文结果包括了拟三角和余拟三角Hopf代数(Hopf群余代数),Doi-Hopf群模等情况. The authors investigate how the category of group entwined modules can be made into a monoidal category.It suffices that the algebra and 7r-coalgebra in question are bialge- bra and semi-Hopf 7r-coalgebra,with some extra compatibility relation.Braidings on a monoidal category of 7r-entwined modules are constructed.The construction unifies quasitriangular and coquasitriangular Hopf algebras（Hopfπ-coalgebras）,Doi-Hopfπ-modules.
作者 刘玲 王栓宏
机构地区 浙江师范大学数理与信息工程学院 东南大学数学系
出处 《数学物理学报（A辑）》 CSCD 北大核心 2010年第6期1612-1620,共9页 Acta Mathematica Scientia
基金 国家自然科学基金(10571026)资助
关键词 群缠绕结构 群缠绕模 辫子张量范畴 群余代数 Group entwining structure Group entwined modules Braided monoidal category π-coalgebra
分类号 O153.3 [理学—基础数学]
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参考文献12

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同被引文献14

  • 1BShm G, Brzezifiski T. Cleft extensions of Hopf algebroids. Appl Categor Structure, 2006, 14:431-469.
  • 2BShm G, Nill F, Szlachanyi K. Weak Hopf algebras I: Integral theory and C*-structure. J Algebra, 1999, 221:385-438.
  • 3Blattner R, Cohen M, Montgomery S. Crossed product and inner actions of Hopf algebras. Trans Amer Math Soc, 1986, 298:671-711.
  • 4Blattner R, Montgomery S. Crossed product and Galois extensions of Hopf algebras. Pacific Journal of Math, 1989, 137:37-54.
  • 5Caenepeel S, De Lombaerde M. A categorical approach to Turaev's Hopf group-coalgebras. Comm Algebra, 2006, 34:2631-2657.
  • 6Shen B L, Wang S H. Blattner-Cohen-Montgomery's duality theorem for (weak) group smash products. Comm Algebra, 2008, 36:2387-2409.
  • 7Shen B L, Wang S H. On group crossed products. Int Electron J Algebra, 2008, 4:177-188 Turaev V. Homotopy field theory in dimension 3 and crossed group-categories. 2000, Preprint arxiv: math GT/0005291.
  • 8Turaev V. Homotopy field theory in dimension 3 and crossed group-categories. 2000, Preprint arxiv: math GT/0005291.
  • 9Virelizier A. Hopf group-coalgebras. J Pure Appl Algebra, 2002, 171:75-122.
  • 10Van Daele A, Wang S H. New braided crossed categories and Drinfel'd quantum double for weak Hopf group coalgebras. Comm Algebra, 2008, 36:2341-2386.

引证文献1

数学物理学报（A辑）
2010年 第6期

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