[1] You Miman, Wang Shuanhong,. Monoidal Hom-Hopf algebra on Hom-twisted product [J]. Journal of Southeast University (English Edition), 2016, 32 (3): 391-394. [doi:10.3969/j.issn.1003-7985.2016.03.022]

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Monoidal Hom-Hopf algebra on Hom-twisted product()

Hom-扭曲积上的monoidal Hom-Hopf代数

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

Volumn:

32

Issue:

2016 3

Page:

391-394

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2016-09-20

Info

Title:

Monoidal Hom-Hopf algebra on Hom-twisted product

Hom-扭曲积上的monoidal Hom-Hopf代数

Author(s):

You Miman;  Wang Shuanhong

Department of Mathematics, Southeast University, Nanjing 211189, China

游弥漫;  王栓宏

东南大学数学系, 南京 211189

Keywords:

monoidal Hom-Hopf algebra;  Hom-twisted product;  Hom-smash coproduct

monoidal Hom-Hopf代数;  Hom-扭曲积;  Hom-冲余积

PACS:

O153.3

DOI:

10.3969/j.issn.1003-7985.2016.03.022

Abstract:

Let(H, α)be a monoidal Hom-bialgebra and(B, β)be a left(H, α)-Hom-comodule coalgebra. The new monoidal Hom-algebra B^#_×H is constructed with a Hom-twisted product B_σσ［H］ and a B×H Hom-smash coproduct. Moreover, a sufficient and necessary condition for B^#_×H to be a monoidal Hom-bialgebra is given. In addition, let(H, α)be a Hom-σ-Hopf algebra with Hom-σ-antipode S_HH, and a sufficient condition for this new monoidal Hom-bialgebra B^#_×H with the antipode S defined by S(b×h)=(1_BB×S_HH(α^-1(b_(-1))))·(S_BB(b₍₀₎)×1_HH)to be a monoidal Hom-Hopf algebra is derived.

设(H, α)是monoidal Hom-Hopf代数, (B, β)是左(H, α)-Hom-余模余代数.构造了由Hom-扭曲积B_σ［H］和Hom-冲余积B×H构成的新monoidal Hom-代数B^#_×H.并给出了B^#_×H成为monoidal Hom-双代数的充分必要条件B^#_×H.此外, 设(H, α)是带有Hom-σ-反对极S_H的Hom-σ-Hopf 代数, 并找到此monoidal Hom-双代数B^#_×H带有定义为S(b×h)=(1_BB×S_H(α^-1(b_(-1))))(S_B(b₍₀₎)×1_HH)的反对极S成为monoidal Hom-Hopf 代数的充分条件.

References:

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[4] Lu Daowei, Wang Shuanhong. Crossed product and Galois extension of monoidal Hom-Hopf algebras [EB/OL].(2014-05-29). http://arxiv.org/abs/1405.7528.
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Memo

Memo:

Biographies: You Miman(1984—), female, doctor; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088, 10871042, 11571173), the Fundamental Research Funds for the Central Universities(No.KYLX15_0105).
Citation: You Miman, Wang Shuanhong.Monoidal Hom-Hopf algebra on Hom-twisted product[J].Journal of Southeast University(English Edition), 2016, 32(3):391-394.DOI:10.3969/j.issn.1003-7985.2016.03.022.

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