[1] You Miman, Lu Daowei, Wang Shuanhong,. Crossed products for Hopf group-algebras [J]. Journal of Southeast University (English Edition), 2021, 37 (3): 339-342. [doi:10.3969/j.issn.1003-7985.2021.03.015]

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

37

Issue:

2021 3

Page:

339-342

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2021-09-20

Info

Title:

Crossed products for Hopf group-algebras

Author(s):

You Miman¹;  Lu Daowei²;  Wang Shuanhong³

¹School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450045, China
²Department of Mathematics, Jining University, Qufu 273155, China
³School of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

Hopf π-algebra;  cleft extension theorem;  π-comodule-like algebra;  group crossed products

PACS:

O153

DOI:

10.3969/j.issn.1003-7985.2021.03.015

Abstract:

First, the group crossed product over the Hopf group-algebras is defined, and the necessary and sufficient conditions for the group crossed product to be a group algebra are given. The cleft extension theory of the Hopf group algebra is introduced, and it is proved that the crossed product of the Hopf group algebra is equivalent to the cleft extension. The necessary and sufficient conditions for the crossed product equivalence of two Hopf groups are then given. Finally, combined with the equivalence theory of the Hopf group crossed product and cleft extension, the group crossed product constructed by the general 2-cocycle as algebra is determined to be isomorphic to the group crossed product of the 2-cocycle with a convolutional invertible map of the 2-cocycle. The unit property of a general 2-cocycle is equivalent to the convolutional invertible map of the 2-cocycle, and the combination condition of the weak action is equivalent to the convolutional invertible map of the 2-cocycle and the combination condition of the weak action. Similarly, crossed product algebra constructed by the general 2-cocycle is isomorphic to the Hopf π-crossed product algebra constructed by the 2-cocycle with a convolutional invertible map.

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Memo

Memo:

Biographies: You Miman(1984—), female, doctor, lecturer; Lu Daowei(corresponding author), male, doctor, associate professor, ludaowei620@126.com.
Foundation item: The National Natural Science Foundation of China(No. 11871144, 11901240).
Citation: You Miman, Lu Daowei, Wang Shuanhong.Crossed products for Hopf group-algebras[J].Journal of Southeast University(English Edition), 2021, 37(3):339-342.DOI:10.3969/j.issn.1003-7985.2021.03.015.

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