| 量子群胚上的smash余积对偶定理 |
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| 引用本文： | 周璇,刘玲,王栓宏.量子群胚上的smash余积对偶定理[J].东南大学学报,2010(4):647-650. |
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| 作者姓名： | 周璇 刘玲 王栓宏 |
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| 作者单位： | [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 |
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| 基金项目： | The National Natural Science Foundation of China（No.10871042）; the Natural Science Foundation of Jiangsu Province（No.BK2009258） |
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| 摘 要： | 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＊）.
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| 关 键 词： | 弱Hopf代数（量子群胚） 弱广义smash余积 弱模余代数 弱余模余代数 弱双模余代数 对偶定理 |
Duality theorem for smash coproduct over quantum groupoids |
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| Zhou XuanLiu LingWang Shuanhong.Duality theorem for smash coproduct over quantum groupoids[J].Journal of Southeast University(English Edition),2010(4):647-650. |
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| Authors: | Zhou XuanLiu LingWang Shuanhong |
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| Institution: | Zhou XuanLiu LingWang Shuanhong(1Department of Mathematics,Southeast University,Nanjing 211189,China)(2College of Mathematics Physics and Information Engineering,Zhejiang Normal University,Jinhua 321004,China) |
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| Abstract: | 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. |
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| Keywords: | weak Hopf algebras（quantum groupoids） weak generalized smash coproducts weak module coalgebras weak comodule coalgebras weak bimodule coalgebras duality theorem |
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