论文标题
HOM-HOPF代数的四角啤酒花模块
Four-angle Hopf modules for Hom-Hopf algebras
论文作者
论文摘要
我们介绍了HOM-HOPF代数$（H，β）$的四角$ H $ -HOPF模块的概念，并表明类别$ \！ $ \ otimes_ {h} $或hom-cotensor产品$ \ box_ {h} $作为单型产品。我们研究类别$ \ MATHCAL {yd}^{h} _ {h} $ atter-drinfel'd模块带有丝构成图的模块可以组织为编织的单体类别，我们使用新的单体结构并在其中使用新的单体结构，并证明该类别的braiding是$ $ \ y Mathcal $ \ yd}^yd {对称然后$（H，β）$是微不足道的。然后，我们证明了单体类别$（〜\！^{h} _ { $（〜\！此外，我们给出了单体类别的编织结构$（〜\！^{h} _ { $（〜\！最后，我们证明，当$（h，β）$是有限的尺寸hom-hopf代数时，类别$ \！ h^{*} \＃h \ otimes h^{op} $。
We introduce the notion of a four-angle $H$-Hopf module for a Hom-Hopf algebra $(H,β)$ and show that the category $\!^{H}_{H}\mathfrak{M}^{H}_{H}$ of four-angle $H$-Hopf modules is a monoidal category with either a Hom-tensor product $\otimes_{H}$ or a Hom-cotensor product $\Box_{H}$ as a monoidal product. We study the category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules with bijective structure map can be organized as a braided monoidal category, in which we use a new monoidal structure and prove that if the canonical braiding of the category $\mathcal{YD}^{H}_{H}$ is symmetry then $(H,β)$ is trivial. We then prove an equivalence between the monoidal category $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ or $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$ of four-angle $H$-Hopf modules, and the monoidal category $\mathcal{YD}^{H}_{H}$ of Yetter-Drinfel'd modules, and furthermore, we give a braiding structure of the monoidal categorys $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\otimes_{H})$ (and $(~\!^{H}_{H}\mathfrak{M}^{H}_{H},\Box_{H})$). Finally, we prove that when $(H,β)$ is finite dimensional Hom-Hopf algebra, the category $\!^{H}_{H}\mathfrak{M}^{H}_{H}$ is isomorphic to the representation category of Heisenberg double $H^{*op}\otimes H^{*}\#H\otimes H^{op}$.
