[1] Zhou Xuan, Liu Ling, Wang Shuanhong,. Duality theorem for smash coproduct over quantum groupoids [J]. Journal of Southeast University (English Edition), 2010, 26 (4): 647-650. [doi:10.3969/j.issn.1003-7985.2010.04.030]
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Duality theorem for smash coproduct over quantum groupoids(
)
量子群胚上的smash余积对偶定理
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 26
- Issue:
- 2010 4
- Page:
- 647-650
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2010-12-30
Info
- Title:
- Duality theorem for smash coproduct over quantum groupoids
- 量子群胚上的smash余积对偶定理
- Author(s):
- Zhou Xuan1; Liu Ling2; Wang Shuanhong1
-
1Department of Mathematics, Southeast University, Nanjing 211189, China
2College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
- Keywords:
- weak Hopf algebras(quantum groupoids); weak generalized smash coproducts; weak module coalgebras; weak comodule coalgebras; weak bimodule coalgebras; duality theorem
- PACS:
- O153.3
- DOI:
- 10.3969/j.issn.1003-7985.2010.04.030
- 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×lHH D over quantum groupoids is defined and the module and comodule structures on it are constructed. The weak generalized right smash coproduct C×rLL 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×rHH D to be isomorphic to C⊗vv 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×lHH H)×lH* H*≅C⊗vv(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×lHH D的定义, 并构造其模和余模结构.类似考虑右广义smash余积C×rLL D.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×rHH D和C⊗vvD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×lHH H)×lH* H*≅C⊗vv(H×lH* H*).
References:
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Memo
- Memo:
-
Biographies: Zhou Xuan(1983—), female, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation items: The National Natural Science Foundation of China(No.10871042), the Natural Science Foundation of Jiangsu Province(No.BK2009258).
Citation: Zhou Xuan, Liu Ling, Wang Shuanhong.Duality theorem for smash coproduct over quantum groupoids[J].Journal of Southeast University(English Edition), 2010, 26(4):647-650.