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FS-coalgebras and crossed coproducts

  • Yuanyuan Chen , Zhongwei Wang und Liangyun Zhang EMAIL logo
Veröffentlicht/Copyright: 15. August 2017
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Abstract

In this paper, we introduce FS-coalgebras, which provide solutions of FS-equations and also solution of braid equations considered by Caenepeel, Militaru and Zhu. FS-coalgebras are constructed by using FS-equations and Harrison cocycles. As applications, we prove that every bialgebra H is an FS-bialgebra if and only if there is a two-sided integral α in H such that ε(α)=1, and we show that the crossed coproduct HR introduced by the Harrison cocycle R is an FS-coalgebra when (H,R) is a finite-dimensional quasitriangular Hopf algebra or a Long copaired bialgebra.

MSC 2010: 16T05

Award Identifier / Grant number: 11401311

Award Identifier / Grant number: 11571173

Award Identifier / Grant number: BK20140676

Award Identifier / Grant number: BK20141358

Funding statement: This work is supported by the Fundamental Research Funds for the Central Universities (No. KJQN201550), the National Natural Science Foundation of China (11401311, 11571173), and the Natural Science Foundation of Jiangsu Province (BK20140676, BK20141358).

Acknowledgements

The authors would like to thank the referee for his/her helpful suggestions.

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Received: 2015-05-29
Revised: 2015-12-12
Accepted: 2016-04-19
Published Online: 2017-08-15
Published in Print: 2019-09-01

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