Double Biproduct Hom-Bialgebra and Related Quasitriangular Structures

查看全文 作　　者：Tianshui [1]MA;Haiying [1]LI;Linlin [1]LIU 机构地区：[1]School of Mathematics and Information Science, Henan Normal University,Xinxiang 453007, Henan, China 出　　处：《Chinese Annals of Mathematics,Series B》索引2016年第37卷第6期,共22页 基　　金：supported by the Henan Provincial Natural Science Foundation of China(No.17A110007);the Foundation for Young Key Teacher by Henan Province(No.2015GGJS-088) 摘　　要：Let(H, β) be a Hom-bialgebra such that β~2= id_H.(A, α_A) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category (_H^H)YD and(B, α_B) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YD_H^H. The authors define the two-sided smash product Hom-algebra(A■H■B, α_A ? β ? α_B) and the two-sided smash coproduct Homcoalgebra(A◇H◇B, α_A ? β ? α_B). Then the necessary and sufficient conditions for(A■H■B, α_A ? β ? α_B) and(A◇H◇B, α_A ? β ? α_B) to be a Hom-bialgebra(called the double biproduct Hom-bialgebra and denoted by(A_◇~■H_◇~■B, α_A ? β ? α_B)) are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra(A◇H, α_A ? β) to be quasitriangular are given. 关 键 词：两倍 biproduct Hom-Yetter-Drinfeld 范畴 Radfords biproduct Hom-Yang-Baxter 方程