A+ CATEGORY SCIENTIFIC UNIT

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

Abstract

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.

Authors

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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image