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[1] Zhang Senlin, Wang Shuanhong,. Fundamentals of quasigroup Hopf group-coalgebras [J]. Journal of Southeast University (English Edition), 2021, 37 (1): 114-118. [doi:10.3969/j.issn.1003-7985.2021.01.015]
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
37
Issue:
2021 1
Page:
114-118
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2021-03-20

Info

Title:
Fundamentals of quasigroup Hopf group-coalgebras
Author(s):
Zhang Senlin;  Wang Shuanhong
School of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
Hopf quasigroup;  group-coalgebra;  quasigroup Hopf group-coalgebra;  convolution algebra
PACS:
O153
DOI:
10.3969/j.issn.1003-7985.2021.01.015
Abstract:
A large class of algebras(possibly nonassociative)with group-coalgebraic structures, called quasigroup Hopf group-coalgebras, is introduced and studied. Quasigroup Hopf group-coalgebras provide a unifying framework for the classical Hopf algebras and Hopf group-coalgebras as well as Hopf quasigroups. Then, basic results similar to those in Hopf algebras H are proved, such as anti-(co)multiplicativity of the antipode S:H→H, and S2=id if H is commutative or cocommutative.

References:

[1] Turaev V. Homotopy field theory in dimension 3 and crossed group-categories[J/OL]. arXiv: math/0005291.2000. https: //arxiv.org/abs/math/0005291.
[2] Virelizier A. Hopf group-coalgebras[J].Journal of Pure and Applied Algebra, 2002, 171(1): 75-122. DOI:10.1016/S0022-4049(01)00125-6.
[3] Wang S H. Group twisted smash products and doi-Hopf modules for T-coalgebras[J].Communications in Algebra, 2004, 32(9): 3417-3436. DOI:10.1081/AGB-120039402.
[4] Wang S H. Group entwining structures and group coalgebra Galois extensions[J].Communications in Algebra, 2004, 32(9): 3437-3457. DOI:10.1081/AGB-120039403.
[5] Wang S H. A Maschke type theorem for Hopf π-comodules[J]. Tsukuba Journal of Mathematics, 2004, 28(2): 377-388. DOI:10.21099/tkbjm/1496164806.
[6] Zunino M. Double construction for crossed Hopf coalgebras[J].Journal of Algebra, 2004, 278(1): 43-75. DOI:10.1016/j.jalgebra.2004.03.019.
[7] Zunino M. Yetter-Drinfeld modules for crossed structures[J].Journal of Pure and Applied Algebra, 2004, 193(1/2/3): 313-343. DOI:10.1016/j.jpaa.2004.02.014.
[8] Pérez-Izquierdo J M, Shestakov I P. An envelope for Malcev algebras[J].Journal of Algebra, 2004, 272(1): 379-393. DOI:10.1016/S0021-8693(03)00389-2.
[9] Pérez-Izquierdo J M. An envelope for Bol algebras[J].Journal of Algebra, 2005, 284(2): 480-493. DOI:10.1016/j.jalgebra.2004.09.038.
[10] Pérez-Izquierdo J M. Algebras, hyperalgebras, nonassociative bialgebras and loops[J].Advances in Mathematics, 2007, 208(2): 834-876. DOI:10.1016/j.aim.2006.04.001.
[11] Klim J, Majid S. Hopf quasigroups and the algebraic 7-sphere[J].Journal of Algebra, 2010, 323(11): 3067-3110. DOI:10.1016/j.jalgebra.2010.03.011.
[12] Sweedler M E. Hopf algebras[M]. New York: Benjamin, 1969.

Memo

Memo:
Biographies: Zhang Senlin(1989—), male, Ph.D. candidate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088, 11571173, 11871144), the Natural Science Foundation of Jiangsu Province(No.BK20171348).
Citation: Zhang Senlin, Wang Shuanhong.Fundamentals of quasigroup Hopf group-coalgebras[J].Journal of Southeast University(English Edition), 2021, 37(1):114-118.DOI:10.3969/j.issn.1003-7985.2021.01.015.
Last Update: 2021-03-20