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Representations and categorical realization of Hom-quasi-Hopf algebras
  • 期刊名称：Front. Math. China
  • 时间：2015.2.5
  • 页码：1263-1281
  • 分类：O153.3[理学—数学;理学—基础数学] TP311[自动化与计算机技术—计算机软件与理论;自动化与计算机技术—计算机科学与技术]
  • 作者机构：[1]School of Mathematics and Statistics and Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, China, [2]School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
  • 相关基金：Acknowledgements The authors would like to thank the referees for a number of helpful comments that greatly improved the presentation of this paper. The first author also thanks Prof. Ke Wu and Prof. Shikun Wang for stimulating discussion and help in preparation of this paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11047030, 11171055, 11571145） and the Science and Technology Program of Henan Province （No. 152300410061）.
  • 相关项目：模李超代数及相关代数的结构与分类
作者： Cheng Yongsheng|Zhang Xiugu|
关键词： HOPF代数, 分类, 陈述, 余代数, 类模块, 双代数, 同构, 公理, Monoidal category, Hom-coassociative 2-coalgebra, Hom-quasiHopf algebra
中文摘要：

我们由在 comultiplication 地图上强加 Hom-coassociative 法律直到一些同晶型并且要求这些同晶型满足 copentagon 公理并且获得 Hom-coassociative 2-coalgebra 把一条 monoidal 范畴途径给 Hom-coassociative coalgebra，它是一个 2- 范畴。第二，我们以他们模块的范畴描绘 Hom-bialgebras。最后，我们用 Hom-coassociative 2-coalgebra 给 Hom-quasi-Hopf 代数学的一条范畴的认识。

英文摘要：

We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.

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