Duality theorem for smash coproduct over quantum groupoids  

量子群胚上的smash余积对偶定理(英文)

作　　者：周璇[1] 刘玲[2] 王栓宏[1] 

机构地区：[1]东南大学数学系,南京211189 [2]浙江师范大学数理信息学院,金华321004

出　　处：《Journal of Southeast University(English Edition)》2010年第4期647-650,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.10871042);the Natural Science Foundation of Jiangsu Province(No.BK2009258)

摘　　要：The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.研究了量子群胚上与弱模余代数和余模余代数相关的弱广义smash余积的对偶定理.设H是弱Hopf代数,C是弱左H余模余代数,D是弱左H模余代数.首先,给出量子群胚上的弱广义smash余积C×lHD的定义,并构造其模和余模结构.类似考虑右广义smash余积C×LrD.然后得到它们之间的同构.其次,通过引入弱卷积逆,弱余内作用和强相关余内作用的概念,得到C×HrD和CvD同构的充分条件,其中v∈WC(C,H),H在D上的余作用是右强相关余内作用.最后,证明了量子群胚上广义smash余积的对偶定理:(C×HlH)×lH*H*≌Cv(H×lH*H*).

关 键 词：weak Hopf algebras（quantum groupoids） weak generalized smash coproducts weak module coalgebras weak comodule coalgebras weak bimodule coalgebras duality theorem 

分 类 号：O153.3[理学—数学]