Hom-Hopf代数上的余代数结构

The Coalgebra Structure over Hom-Hopf Algebra

中文关键词:  Hom-Hopf代数  Hom-$\omega$-交叉余积  $\omega$-交叉余积

英文关键词:Hom-Hopf algebra  Hom-$\omega$-crossed coproduct  $\omega$-crossed coproduct

中文摘要:

      设$(C,\alpha)$和$(H,\beta)$是Hom-双代数,$\omega:C\otimes H\rightarrow H\otimes C$是一个线性映射.该文定义了Hom-$\omega$-交叉余积$(C_{\omega}\bowtie_{\sigma} H,\gamma)$ 并给出了它是Hom-Hopf代数的充分必要条件.

英文摘要:

      Let $(C,\alpha)$ and $(H,\beta)$ be Hom-bialgebras and $\omega:C\otimes H\rightarrow H\otimes C$ a linear map. We introduce the concept of a Hom-$\omega$-crossed coproduct $(C_{\omega}\bowtie_{\sigma} H,\gamma)$ and we give necessary and sufficient conditions for the new object to be a Hom-Hopf algebra.