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[1] Yan Dongdong, Wang Shuanhong,. Diagonal crossed product of multiplier Hopf algebras [J]. Journal of Southeast University (English Edition), 2020, 36 (2): 241-244. [doi:10.3969/j.issn.1003-7985.2020.02.016]
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Diagonal crossed product of multiplier Hopf algebras()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
36
Issue:
2020 2
Page:
241-244
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2020-06-20

Info

Title:
Diagonal crossed product of multiplier Hopf algebras
Author(s):
Yan Dongdong;  Wang Shuanhong
School of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
multiplier Hopf algebra;  bimodule algebra;  diagonal crossed product
PACS:
O153
DOI:
10.3969/j.issn.1003-7985.2020.02.016
Abstract:
Let A and B be two regular multiplier Hopf algebras. First, the notion of diagonal crossed product B#A of multiplier Hopf algebras is constructed using the bimodule algebra, which is a generalization of the diagonal crossed product in the sense of Hopf algebras. The result that the product in B#A is non-degenerate is given. Next, the definition of the comultiplication Δ# on B#A is introduced, which is composed of the multiplier ΔBB(b)on BB and the multiplier ΔAA(a)on AA, and the element Δ#(ba)is a two-side multiplier of B#AB#A, for any b∈B and a∈A. Then, a sufficient condition for B#A to be a regular multiplier Hopf algebra is described. In particular, Delvaux’s main theorem in the case of smash products is generalized. Finally, these integrals on a diagonal crossed product of multiplier Hopf algebras are considered.

References:

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Memo

Memo:
Biographies: Yan Dongdong(1992—), male, graduate; Wang Shuanhong(corresponding author), male, doctor, professor, shuanhwang@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371088, 11571173, 11871144), the Natural Science Foundation of Jiangsu Province(No.BK20171348).
Citation: Yan Dongdong, Wang Shuanhong. Diagonal crossed product of multiplier Hopf algebras.[J].Journal of Southeast University(English Edition), 2020, 36(2):241-244.DOI:10.3969/j.issn.1003-7985.2020.02.016.
Last Update: 2020-06-20