Abstract
In this paper we study the new notion of a symmetric pair of objects in the Yetter–Drinfeld category over a weak Hopf algebra H with a bijective antipode. Then we show that the (co)commutativity and trivial property of H are determined by some symmetric pairs of objects in
, generalizing the main results in Cohen and Westreich and Pareigis. Finally, we study the u-condition generalizing the corresponding results appeared in Cohen and Westreich.
ACKNOWLEDGMENTS
The authors would like to thank the referee for her/his comments.
Notes
Communicated by M. Cohen.