| 郑乃峰.Hom-$\omega$-smash 积Hopf 代数的拟三角结构[J].数学年刊A辑,2013,34(6):689~708 |
| Hom-$\omega$-smash 积Hopf 代数的拟三角结构 |
| The Quasi-triangular Structures of Hom-!-smash Product Hopf Algebra |
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| DOI： |
| 中文关键词: Hom-Hopf 代数, 拟三角 Hom-Hopf 代数, Hom-$\omega$-smash 积 |
| 英文关键词:Hom-Hopf algebra, Quasi-triangular Hom-Hopf algebra, Hom-ω-
smash product |
| 基金项目:宁波市自然科学基金 (No.2011A610172) |
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| 中文摘要: |
| 设 $(A,\alpha)$和$(H,\beta)$ 是 Hom-\!\!双代数, $\omega:H\otimes A\rightarrow A\otimes H$ 是线性映射,
定义了 Hom-$\omega$-smash 积$(A\sharp_{\omega} H,\gamma)$,并给出了 $(A\bowtie_{\omega}H,\gamma)$
是 Hom-bialgebra 的充要条件. 最后,研究了$(A\bowtie_{\omega} H,\gamma)$上的拟三角结构, 并给出了它是拟
三角 Hom-Hopf 代数的充要条件. |
| 英文摘要: |
| Let $(A,\alpha)$ and $(H,\beta)$
be Hom-bialgebras and $\omega:H\otimes A\rightarrow A\otimes H$ a
linear map. The author introduces a Hom-$\omega$-smash product
$(A\sharp_{\omega}H,\gamma)$ and gives necessary and sufficient
conditions for $(A\bowtie_{\omega}\!\!H,\gamma)$ to be a Hom-bialgebra.
The author studies the quasi-triangular structures over Hom-$\omega$-smash
product Hopf algebras $(A\bowtie_{\omega}\!\!H,\gamma)$. The author shows the
necessary and sufficient conditions for $(A\bowtie_{\omega}H,\gamma,R)$ to be a quasi-trian-gular Hom-Hopf algebra. |
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