Braided groups and quantum groupoids

被引：2

作者：

Liu, G. H. ^{[1
]}

Zhu, H. X. ^{[2
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Univ Hasselt, Dept Math, B-3590 Diepenbeek, Belgium

来源：

ACTA MATHEMATICA HUNGARICA | 2012年 / 135卷 / 04期

关键词：

quantum groupoid; weak Hopf algebra; braided group; braided Hopf algebra; HOPF-ALGEBRAS; FACE ALGEBRAS;

D O I：

10.1007/s10474-011-0183-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H be a quasitriangular weak Hopf algebra. It is proved that the centralizer subalgebra of its source subalgebra in H is a braided group (or Hopf algebra in the category of left H-modules), which is cocommutative and also a left braided Lie algebra in the sense of Majid.

引用

页码：383 / 399

页数：17

共 15 条

[1]

[Anonymous], 1995, QUANTUM GROUPS

[2] Weak Hopf algebras I.: Integral theory and C*-structure [J].

Böhm, G ;

Nill, F ;

Szlachányi, K .

JOURNAL OF ALGEBRA, 1999, 221 (02) :385-438

[3]

BOHM G, 1996, LETT MATH PHYS, V35, P437

[4] On fusion categories [J].

Etingof, P ;

Nikshych, D ;

Ostrik, V .

ANNALS OF MATHEMATICS, 2005, 162 (02) :581-642

[5] Braided Lie algebras and bicovdriant differential calculi over co-quasitriangular Hopf algebras [J].

Gomez, X ;

Majid, S .

JOURNAL OF ALGEBRA, 2003, 261 (02) :334-388

[6] Face algebras I - A generalization of quantum group theory [J].

Hayashi, T .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1998, 50 (02) :293-315

[7] Face algebras and unitarity of SU(N)L-TQFT [J].

Hayashi, T .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 203 (01) :211-247

[8] QUANTUM GROUP SYMMETRY OF PARTITION-FUNCTIONS OF IRF MODELS AND ITS APPLICATION TO JONES INDEX THEORY [J].

HAYASHI, T .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 157 (02) :331-345

[9] TRANSMUTATION THEORY AND RANK FOR QUANTUM BRAIDED GROUPS [J].

MAJID, S .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1993, 113 :45-70

[10] BRAIDED GROUPS AND ALGEBRAIC QUANTUM-FIELD THEORIES [J].

MAJID, S .

LETTERS IN MATHEMATICAL PHYSICS, 1991, 22 (03) :167-175

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