一类广义双积及其相关的Yetter-Drinfeld范畴  

A class of generalized biproduct and related Yetter-Drinfeld category

作　　者：马天水[1] 杨海燕 Ma Tianshui;Yang Haiyan(School of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：[1]河南师范大学数学与信息科学学院,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2021年第4期18-23,共6页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11801150);河南省自然科学基金(212300410365);河南师范大学研究生科研创新资助项目(YL202019).

摘　　要：首先给出了广义smash积monoidal BiHom-代数(B#^(m)_(n)H,αB■αH,βB■βH)和广义smash余积monoidal BiHom-余代数(B×^(p)_(q)H,αB■αH,βB■βH),进而得到了由(B#^(m)_(n)H,αB■αH,βB■βH)和(B×^(p)_(q)H,αB■αH,βB■βH)构成monoidal BiHom-双代数(B^(#m,p)_(×n,q)H,αB■αH,βB■βH)的充分必要条件.最后构造了一类与(B^(#m,p)×_(n,q)H,αB■αH,βB■βH)相关的张量范畴.In this article,firstly,we introduce the notions of a generalized smash product MBH-algebra((B#^(m)_(n)H,αB■αH,βB■βH)and a generalized smash coproduct MBH-coalgebra(B×^(p)_(q)H,αB■αH,βB■βH).Furthermore,we get the necessary and sufficient conditions for(B#^(m)_(n)H,αB■αH,βB■βH)and(B×^(p)_(q)H,αB■αH,βB■βH)to be a MBH-bialgebras(B^(#m,p)_(×n,q)H,αB■αH,βB■βH).At last,we provide a class of monoidal category which is related to(B^(#m,p)×_(n,q)H,αB■αH,βB■βH).

关 键 词：Radford双积 BiHom-代数 YETTER-DRINFELD范畴 

分 类 号：O153.3[理学—数学]