JournalsrsmupVol. 130pp. 127–145

Hopf π\pi-Crossed Biproduct and Related Coquasitriangular Structures

  • Tianshui Ma

    Henan Normal University, Xinxiang, China
  • Yanan Song

    Henan Normal University, Xinxiang, China
Hopf $\pi$-Crossed Biproduct and Related Coquasitriangular Structures cover
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Abstract

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

Cite this article

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

DOI 10.4171/RSMUP/130-3