构造群缠绕模范畴成为辫子张量范畴

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1612-1620.

构造群缠绕模范畴成为辫子张量范畴

刘玲¹|王栓宏²

1.浙江师范大学数理与信息工程学院浙江金华 321004|2.东南大学数学系南京 210096

收稿日期:2008-09-18 修回日期:2009-10-19 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
国家自然科学基金(10571026)资助

Making the Category of Group Entwined Modules into a Bradied Monoidal Category

LIU Ling¹, WANG Shuan-Hong²

1.College of Mathematical Physics and Information Engineering, Zhejiang Normal University, Zhejiang Jinhua 321004;
2.Department of Mathematics, Southeast University, Nanjing 210096

Received:2008-09-18 Revised:2009-10-19 Online:2010-12-25 Published:2010-12-25
Supported by:
国家自然科学基金(10571026)资助

摘要/Abstract

摘要：

该文研究了群缠绕模范畴怎样构造成张量范畴^[11], 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.

关键词: 群缠绕结构, 群缠绕模, 辫子张量范畴, 群余代数

Abstract:

The authors investigate how the category of group entwined modules can be made into a monoidal category^[11]. It suffices that the algebra and π-coalgebra in question are bialgebra and semi-Hopf π-coalgebra, with some extra compatibility relation. Braidings on a monoidal
category of π-entwined modules are constructed. The construction unifies quasitriangular and coquasitriangular Hopf algebras (Hopf π-coalgebras), Doi-Hopf π-modules.

Key words: Group entwining structure, Group entwined modules, Braided monoidal category, π-coalgebra

中图分类号:

16W30

刘玲, 王栓宏. 构造群缠绕模范畴成为辫子张量范畴[J]. 数学物理学报, 2010, 30(6): 1612-1620.

LIU Ling, WANG Shuan-Hong. Making the Category of Group Entwined Modules into a Bradied Monoidal Category[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1612-1620.

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