[1] Yang Tao, Wang Shuanhong,. π-quasitriangular group-cograded multiplier Hopf algebras [J]. Journal of Southeast University (English Edition), 2009, 25 (4): 552-556. [doi:10.3969/j.issn.1003-7985.2009.04.029]
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π-quasitriangular group-cograded multiplier Hopf algebras(
)
)Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]
- Volumn:
- 25
- Issue:
- 2009 4
- Page:
- 552-556
- Research Field:
- Mathematics, Physics, Mechanics
- Publishing date:
- 2009-12-30
Info
- Title:
- π-quasitriangular group-cograded multiplier Hopf algebras
- Author(s):
- Yang Tao; Wang Shuanhong
- Department of Mathematics, Southeast University, Nanjing 211189, China
- PACS:
- O153.3
- DOI:
- 10.3969/j.issn.1003-7985.2009.04.029
- Abstract:
- Let G be a group and 〈A, B〉 be a pair of multiplier Hopf algebras, where B is regular G-cograded. Let π be a crossing action of G on B, Dπ=Acop∝(~overB)=⊕p∈GDπp with Dπp=Acop∝(~overB)p is the Drinfeld double of the pair 〈A, B〉, and then the deformation(~overD)π becomes a multiplier Hopf algebra. B⊗A can be considered as a subalgebra of M(Dπ⊗Dπ), the image of element b⊗a in B⊗A is(1∝b)⊗(a∝1)in M(Dπ⊗Dπ). LetW=∑αWα∈M(B⊗A)be a π-canonical multiplier for the pair 〈A, B〉 with Wα∈M(Bα⊗A)for all α∈G. The image of W in M(Dπ⊗Dπ)is a π-quasitriangular structure over Dπ.
References:
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[3] Abd El-Hafez A T, Delvaux L, Van Daele A. Group-cograded multiplier Hopf(*-)algebra[J]. Algebras and Representation Theory, 2007, 10(1): 77-95.
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[6] Delvaux L, Van Daele A, Wang S H. Quasitriangular(G-cograded)multiplier Hopf algebras[J]. Journal of Algebra, 2005, 289(2): 484-514.
[7] Delvaux L, Van Daele A. The Drinfeld double for group-cograded multiplier Hopf algebras[J]. Algebras and Representation Theory, 2007, 10(3): 197-221.
[8] Delvaux L, Van Daele A. The Drinfeld double versus the Heisenberg double for an algebraic quantum group[J]. Journal of Pure and Applied Algebra, 2004, 190(1): 59-84.
Memo
- Memo:
-
Biographies: Yang Tao(1984—), male, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang2002@yahoo.com.
Foundation items: Specialized Research Fund for the Doctoral Program of Higher Education(No.20060286006), the National Natural Science Foundation of China(No.10871042).
Citation: Yang Tao, Wang Shuanhong. π-quasitriangular group-cograded multiplier Hopf algebras[J]. Journal of Southeast University(English Edition), 2009, 25(4): 552-556.