Abstract
Let H be a triangular Hopf coquasigroup with bijective antipode and B a cotriangular Hopf coquasigroup with bijective antipode. Under some favorable conditions, the aim of this paper is to find some objects satisfying the double centralizer property for any Hopf coquasigroup A which can be written as a tensor product Hopf coquasigroup As a consequence of our theory, both Schur’s double centralizer theorems for triangular and cotriangular Hopf algebras can be obtained. Our main result provides a new approach to construct more objects which have double centralizer property too.
Acknowledgments
The authors are very grateful to the anonymous referee for his/her thorough review of this work and his/her comments and suggestions which help to improve the first version of this paper.