[1] Zhao Xiaofan, Wang Shuanhong,. A note on ribbon elements of Hopf group-coalgebras [J]. Journal of Southeast University (English Edition), 2015, 31 (2): 294-296. [doi:10.3969/j.issn.1003-7985.2015.02.024]

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A note on ribbon elements of Hopf group-coalgebras()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

31

Issue:

2015 2

Page:

294-296

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2015-06-20

Info

Title:

A note on ribbon elements of Hopf group-coalgebras

Author(s):

Zhao Xiaofan;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

quasitriangular Hopf G-coalgebra;  G-grouplike element;  ribbon element;  Drinfeld element

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2015.02.024

Abstract:

Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.

References:

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[5] Turaev V G. Homotopy field theory in dimension 3 and crossed group-categories[EB/OL].(2000)[2013-07-01].http://arxiv.org/abs/math/0005291.
[6] Virelizier A. Hopf group-coalgebras [J]. J Pure Appl Algebra, 2002, 171(1): 75-122.
[7] Virelizier A. Graded quantum groups and quasitriangular Hopf group-coalgebras [J]. Comm Algebra, 2004, 33(9): 3029-3050.
[8] Wang S H. Group entwining structures and group coalgebras Galois extensions [J]. Comm Algebra, 2004, 32(9): 3417-3436.
[9] Wang S H. Group twisted smash products and Doi-Hopf modules for T-coalgebras [J]. Comm Algebra, 2004, 32(9): 3437-3458.

Memo

Memo:

Biographies: Zhao Xiaofan(1986—), female, graduate; Wang shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088), the Natural Science Foundation of Jiangsu Province(No.BK2012736), the Fundamental Research Funds for the Central Universities(No.KYZZ0060).
Citation: Zhao Xiaofan, Wang Shuanhong.A note on ribbon elements of Hopf group-coalgebras[J].Journal of Southeast University(English Edition), 2015, 31(2):294-296.[doi:10.3969/j.issn.1003-7985.2015.02.024]

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