Double centralizer properties related to (co)triangular Hopf coquasigroups

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 a...

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Bibliographic Details
Published in:Communications in algebra 2021-02, Vol.49 (2), p.662-686
Main Authors: Gu, Yue, Wang, Shuanhong
Format: Article
Language:English
Subjects:
(co)triangular Hopf coquasigroup
Antipodes
Braided Lie algebra
double centralizer property
Tensors
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2020.1814792