Representations and categorical realization of Hom-quasi-Hopf algebras  

作　　者：Yongsheng CHENG Xiufu ZHANG 

机构地区：[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

出　　处：《Frontiers of Mathematics in China》2015年第6期1263-1281,共19页中国高等学校学术文摘·数学（英文）

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）.

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.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.

关 键 词：Monoidal category Hom-coassociative 2-coalgebra Hom-quasiHopf algebra 

分 类 号：O153.3[理学—数学] TP311[理学—基础数学]