[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()

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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

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×^l_HH D over quantum groupoids is defined and the module and comodule structures on it are constructed. The weak generalized right smash coproduct C×^r_LL 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×^r_HH 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×^l_HH H)×^l_H^* H^*≅C⊗_vv(H×^l_H^* H^*), is obtained.

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.

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