基于Benson-Carlson商环的双Frobenius代数的构造  

Construction of bi-Frobenius algebras via the Benson-Carlson quotient rings

作　　者：王志华 李立斌[3] Yinhuo Zhang Zhihua Wang, Libin Li ＆ Yinhuo Zhang

机构地区：[1]泰州学院数理学院,泰州225300 [2]南京大学数学系,南京210093 [3]扬州大学数学科学学院,扬州225002 [4]Department of Mathematics and Statistics,University of Hasselt,Diepeenbeek 3590,Belgium

出　　处：《中国科学：数学》2018年第4期471-482,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号：11471282); 中国博士后基金(批准号：2017M610316)资助项目

摘　　要：设H为有限维球面(spherical)Hopf代数,r(H)为H的Green环,P为量子维数为0的H-模的同构类生成的r(H)的理想.本文利用可除(negligible)态射空间的维数在r(H)上定义了一个双线性型.该双线性型为结合、对称双线性型并且双线性型的根为r(H)中某中心元的零化理想.然后讨论了Green环r(H)的一类商环,即所谓的Benson-Carlson商环r(H)/P.该商环可以视为H-模范畴的一类商范畴的Green环.进一步,如果H作为代数还是有限表示型的,那么Benson-Carlson商环r(H)/P具有类群代数和双Frobenius代数结构.Let H be a finite dimensional spherical Hopf algebra, r（H） the Green ring of H and P the ideal of r（H） generated by all H-modules of quantum dimension zero. Using dimensions of negligible morphism spaces,we define a bilinear form on the Green ring r（H）. This form is associative, symmetric and its radical is annihilator of a certain central element of r（H）. After that we consider the Benson-Carlson quotient ring r（H）/P of r（H）.This quotient ring can be thought of as the Green ring of a factor category of H-module category. Moreover, if H is of finite representation type, the Benson-Carlson quotient ring admits group-like algebra as well as bi-Frobenius algebra structure.

关 键 词：Green环 球面Hopf代数 类群代数 双Frobenius代数 

分 类 号：O153.3[理学—数学]