Hopf -Crossed Biproduct and Related Coquasitriangular Structures

  • Tianshui Ma

    Henan Normal University, Xinxiang, China
  • Yanan Song

    Henan Normal University, Xinxiang, China

Abstract

Let be a group and \( H=(\{H_{\a }\}, \D, \v, S) \) a Hopf -coalgebra (not nec essarily associative), \( \a \in {\pi} \) . Let be an algebra and a coalgebra. We find the necessary and sufficient conditions on the -crossed product \( A\#^{{\pi} }_{\s } H \) with suitable comultiplication and counit to be a Hopf -coalgebra. Moreover, the necessary and sufficient conditions for a Hopf -crossed product \( A\natural _{\s }^{{\pi} } H \) to be a coquasitriangular Hopf -coalgebra are given. In this case the category \( {}^{A\natural _\s ^{\pi} H}{\cal M} \) of the left -comodules over \( A\natural _\s ^{\pi} H \) is a braided monoidal category.

Cite this article

Tianshui Ma, Yanan Song, Hopf -Crossed Biproduct and Related Coquasitriangular Structures. Rend. Sem. Mat. Univ. Padova 130 (2013), pp. 127–145

DOI 10.4171/RSMUP/130-3