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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()
Hopf拟群上扭曲冲积
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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
Hopf拟群上扭曲冲积
Author(s):
Fang Xiaoli;  Wang Shuanhong
Department of Mathematics, Southeast University, Nanjing 211189, China
方小利;  王栓宏
东南大学数学系, 南京 211189
Keywords:
Hopf quasigroup;  quasimodule;  twisted smashproduct
Hopf拟群;  拟模;  扭曲冲积
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.
为了研究平行球面s7的代数结构, 引进了Hopf拟群上的拟模和双拟模代数的概念, 由于这些概念的公理中模缺少结合性的条件, 通过增加对极的条件来弥补结合性的条件.并通过双拟模代数构造了扭曲冲积的概念, 事实上这种扭曲冲积是Hopf代数上扭曲冲积的推广, 并且证明了扭曲冲积与张量余积成为Hopf拟群的充要条件为当且仅当下列条件(h1→a)⊗h2=(h2→a)⊗h1, (a←S(h1))⊗h2=(a←S(h2))⊗h1成立.所得到的结果推广并改进了Hopf代数上扭曲冲积一些相应的结果.

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