PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

The affineness criterion for quantum Hom-Yetter–Drinfel’d modules

Volume 143 / 2016

Shuangjian Guo, Shengxiang Wang Colloquium Mathematicum 143 (2016), 169-185 MSC: Primary 16T05. DOI: 10.4064/cm6609-12-2015 Published online: 14 December 2015


Quantum integrals associated to quantum Hom-Yetter–Drinfel’d modules are defined, and the affineness criterion for quantum Hom-Yetter–Drinfel’d modules is proved in the following form. Let $(H, \alpha)$ be a monoidal Hom-Hopf algebra, $(A, \beta)$ an $(H, \alpha)$-Hom-bicomodule algebra and $B=A^{\mathop{\rm co}H}$. Under the assumption that there exists a total quantum integral $\gamma: H\rightarrow {\rm Hom}(H,A)$ and the canonical map $\beta: A\otimes_{B}A\rightarrow A\otimes H$, $a\otimes_{B}b\mapsto S^{-1}(b_{[1]})\alpha(b_{[0][-1]}) \otimes \beta^{-1}(a)\beta(b_{[0][0]})$, is surjective, we prove that the induction functor $A\otimes_B-:\widetilde{{\mathscr H}} ({\mathscr M}_k)_{B}\rightarrow {}^H{\mathscr H}{\mathscr Y}{\mathscr D}_A$ is an equivalence of categories.


  • Shuangjian GuoSchool of Mathematics and Statistics
    Guizhou University of Finance and Economics
    Guiyang, 550025, P.R. China
  • Shengxiang WangSchool of Mathematics and Finance
    Chuzhou University
    Chuzhou 239000, P.R. China

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image