Double centralizer properties related to (co)triangular Hopf coquasigroups

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 $H\otimes B.$ 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.

Keywords:

• Braided Lie algebra
• (co)triangular Hopf coquasigroup
• double centralizer property

MATHEMATICS SUBJECT CLASSIFICATIONS (2010):

• 16W30
• 16T05
• 16T25
• 16T05
• 17A32
• 18D10

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.

Additional information

Funding

The second author thanks the financial support of the National Natural Science Foundation of China [Grant Nos. 11871144 and 11571173] and the NNSF of Jiangsu Province [No. BK20171348].