[1] Dong Lihong, Wang Shengxiang, Wang Shuanhong, et al. Structure theorem for Hopf group-coalgebra [J]. Journal of Southeast University (English Edition), 2013, 29 (1): 103-105. [doi:10.3969/j.issn.1003-7985.2013.01.021]

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Structure theorem for Hopf group-coalgebra()

Hopf群余代数的结构定理

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

Volumn:

29

Issue:

2013 1

Page:

103-105

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2013-03-20

Info

Title:

Structure theorem for Hopf group-coalgebra

Hopf群余代数的结构定理

Author(s):

Dong Lihong^{1, 2}, Wang Shengxiang¹, Wang Shuanhong¹

¹Department of Mathematics, Southeast University, Nanjing 211189, China
²College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China

董丽红^{1, 2}, 王圣祥¹, 王栓宏¹

¹东南大学数学系, 南京211189; ²河南师范大学数学与信息科学学院, 新乡453007

Keywords:

Hopf group-coalgebra;  Hopf group-comodule algebra;  two-sided relative Hopf group-comodule

Hopf群余代数;  Hopf群余模余代数;  双边相对Hopf群余模

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2013.01.021

Abstract:

Let π be a group with a unit 1; H is a Hopf π-coalgebra and A is a right π-H-comodule algebra. First, the notion of a two-sided relative(A, H)-Hopf π-comodule is introduced; then it is obtained that Hom^H_AH(M, N)? H and HOM_AA(M, N)are isomorphic as right Hopf π-H-comodules, where Hom^H_AH(M, N)denotes the space of right A-module right H-comodule morphisms and HOM_AA(M, N)denotes the rational space of a space Hom_AA(M, N)of right A-module morphisms. Secondly, the structure theorem of endomorphism algebras of two-sided relative(A, H)-Hopf π-comodules is established; that is, End^HH_AA(M)#H and END_AA(M, N)are isomorphic as right Hopf π-H-comodules and algebras.

设π是一个带有单位元1的群, H是一个Hopf π-余代数, A是一个右π-H-余模代数. 首先, 引入双边相对(A, H)-Hopf π-余模的概念, 进而得到了Hom^H_AH(M, N)?H和HOM_AA(M, N)作为右Hopf π-H-余模是同构的结论, 其中Hom^H_AH(M, N)表示右A-模和右H-余模同态作成的空间, HOM_AA(M, N)表示右A-模同态构成空间Hom_AA(M, N)的有理空间. 其次, 得到了双边相对(A, H)-Hopf π-余模的自同态代数的结构定理, 即 End^H_AH(M)#H和END_AA(M, N)作为右Hopf π-H-余模和代数是同构的.

References:

[1] Doi Y. On the structure of relative Hopf module[J]. Comm Algebra, 1983, 11(3): 243-255.
[2] Ulbrich L H. Smash products and comodules of linear maps[J]. Tsukuba J Math, 1990, 14(2): 371-378.
[3] Turaev V. Homotopy quantum field theory[M]. Zürich, Switzerland: European Mathematical Society, 2010.
[4] Virelizier A. Hopf group-coalgebras[J]. J Pure Appl Algebra, 2002, 171: 75-122.
[5] Wang S H. Group twisted smash products and Doi-Hopf modules for T-coalgebras[J]. Comm Algebra, 2004, 32(9): 3417-3436.
[6] Wang S H. Group entwining structures and group coalgebra Galois extensions[J].Comm Algebra, 2004, 32(9): 3437-3457.
[7] Wang S H. Morita contexts, π-Galois extensions for Hopf π-coalgebras[J]. Comm Algebra, 2006, 34(2): 521-546.
[8] Sweedler M. Hopf algebras[M]. New York: Benjamin, 1969.

Memo

Memo:

Biographies: Dong Lihong(1980—), female, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation items: The Research and Innovation Project for College Graduates of Jiangsu Province(No.CXLX_0094), the Natural Science Foundation of Chuzhou University(No.2010kj006Z).
Citation: Dong Lihong, Wang Shengxiang, Wang Shuanhong. Structure theorem for Hopf group-coalgebra.[J].Journal of Southeast University(English Edition), 2013, 29(1):103-105.[doi:10.3969/j.issn.1003-7985.2013.01.021]

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