Rendiconti del Seminario Matematico della Università di Padova


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Volume 130, 2013, pp. 127–145
DOI: 10.4171/RSMUP/130-3

Hopf $\pi$-Crossed Biproduct and Related Coquasitriangular Structures

Tianshui Ma[1] and Yanan Song[2]

(1) College of Mathematics and Information Science, Henan Normal University, 453007, Xinxiang, China
(2) College of Mathematics and Information Science, Henan Normal University, 453007, Xinxiang, China

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

Keywords: Braided monoidal category, crossed product

Ma Tianshui, Song Yanan: Hopf $\pi$-Crossed Biproduct and Related Coquasitriangular Structures. Rend. Sem. Mat. Univ. Padova 130 (2013), 127-145. doi: 10.4171/RSMUP/130-3