Turaev辫子群范畴和Doi-Hopf模  

Turaev Braided Group Categories and Doi-Hopf Modules

作　　者：郭双建[1] 张晓辉[2] GUO Shuangjian ZHANG Xiaohui(School of Mathematics and Statistics, Guizhou University of Finance and Economics, Gui yang 550025, China School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong Province, China)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025 [2]曲阜师范大学数学科学学院,山东曲阜273165

出　　处：《吉林大学学报（理学版）》2017年第4期771-778,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11371088);贵州省科技厅项目基金(批准号:黔科合J字[2014]2045;黔科合基础[2016]1021);贵州省高校优秀科技创新人才支持计划(批准号:黔教合KY字[2015]481);2016年贵州财经大学数学重点学科项目

摘　　要：设G是一个群.利用Turaev辫子群范畴的性质,在Doi-Hopf数据(H,A,C)上构造一个Turaev辫子G-范畴,其中H,A,C是Hopf代数.进一步,当C为有限维时,在一簇Smash积代数{A#~HC~*(α)}_(α∈G)上构造一个拟三角Turaev G-余代数A#~HC~*,其表示范畴与_AM^C(H)是同构的.Let Gbe a group,using the properties of Turaev braided group categories,we constructed a Turaev braided G-category over Doi-Hopf datum（H,A,C）,where H,A,C were Hopf algebras.Furthermore,when C was finite-dimensional Hopf algebra,we constructed a quasitriangular Turaev G-coalgebra A#~HC~＊over a family of Smash product algebras{A#~HC~＊（α）}_（α∈G） whose representation category and ~AM_C（H）were isomorphic.

关 键 词：DOI-HOPF模 Turaev G-余代数 Turaev辫子G-范畴 

分 类 号：O153.3[理学—数学]