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[1] Fang Xiaoli, Wang Shuanhong,. Twisted smash product for Hopf quasigroups [J]. Journal of Southeast University (English Edition), 2011, 27 (3): 343-346. [doi:10.3969/j.issn.1003-7985.2011.03.023]
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Twisted smash product for Hopf quasigroups()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
27
Issue:
2011 3
Page:
343-346
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2011-09-30

Info

Title:
Twisted smash product for Hopf quasigroups
Author(s):
Fang Xiaoli;  Wang Shuanhong
Department of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
Hopf quasigroup;  quasimodule;  twisted smashproduct
PACS:
O153
DOI:
10.3969/j.issn.1003-7985.2011.03.023
Abstract:
In order to study algebraic structures of parallelizable sphere s7, the notions of quasimodules and biquasimodule algebras over Hopf quasigroups, which are not required to be associative, are introduced. The lack of associativity of quasimodules is compensated for by conditions involving the antipode. The twisted smash product for Hopf quasigroups is constructed using biquasimodule algebras, which is a generalization of the twisted smash for Hopf algebras. The twisted smash product and tensor coproduct is turned into a Hopf quasigroup if and only if the following conditions(h1→a)⊗h2=(h2→a)⊗h1, (a←S(h1))⊗h2=(a←S(h2))⊗h1 hold. The obtained results generalize and improve the corresponding results of the twisted smash product for Hopf algebras.

References:

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Memo

Memo:
Biographies: Fang Xiaoli(1979—), male, doctor; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.10971188), the Natural Science Foundation of Zhejiang Province(No.Y6110323), Jiangsu Planned Projects for Postdoctoral Research Funds(No.0902081C), Zhejiang Provincial Education Department Project(No.Y200907995), Qiantang Talents Project of Science Technology Department of Zhejiang Province(No.2011R10051).
Citation: Fang Xiaoli, Wang Shuanhong. Twisted smash product for Hopf quasigroups[J].Journal of Southeast University(English Edition), 2011, 27(3):343-346.[doi:10.3969/j.issn.1003-7985.2011.03.023]
Last Update: 2011-09-20