CONSTRUCTION OF A BRAIDED MONOIDAL CATEGORY FOR BRZEZINSKI CROSSED COPRODUCTS OF HOPF π-ALGEBRAS

被引：3

作者：

Ma , Tianshui ^{[1
]}

Li , Haiying ^{[1
]}

Xu , Shaoxian ^{[2
]}

机构：

[1] Henan Normal Univ, Sch Math & Informat Sci, Xinxiang 453007, Peoples R China

[2] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China

来源：

COLLOQUIUM MATHEMATICUM | 2017年 / 149卷 / 02期

基金：

中国博士后科学基金;

关键词：

braided monoidal category; crossed coproduct; quasitriangular Hopf pi-algebra; COALGEBRAS; PRODUCTS;

D O I：

10.4064/cm6987-9-2016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let pi be a group, C, H Hopf pi-algebras, and g(alpha) : H. and T-alpha : C-alpha circle times H-alpha -> H-alpha circle times C-alpha, families of linear maps. We give necessary and sufficient conditions for the family of Brzezinski crossed coproduct coalgebras {C-alpha #(g alpha)(T alpha) H-alpha}(alpha is an element of pi), to be a Hopf pi-algebra. Moreover, necessary and sufficient conditions for the Brzezinski crossed coproduct Hopf pi-algebra C(sic)(T)(g) (pi) H to be quasitriangular are derived, and in this case, the left pi-module category c(sic)(T)(6) M-pi(Pi) is a braided monoidal category.

引用

页码：309 / 323

页数：15