JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (4): 25-31.doi: 10.6040/j.issn.1671-9352.0.2019.158

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First fundamental theorem and Long dimodules for group-graded Hopf algebras

SHI Guo-dong   

  1. School of Mathmatics, Southeast University, Nanjing 211189, Jiangsu, China
  • Published:2020-04-09

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Abstract: Firstly, a new characterization of group-graded Hopf algebras by the Galois maps is introduced. It leads to a new definition of group-graded Hopf algebras. Secondly, Long dimodules on group-graded Hopf algebras are introduced as a tool to get a class of resolutions of D-equation.

Key words: group-graded Hopf algebras, Galois maps, the first fundamental theorem, Long dimodules, D-equation

CLC Number: 

  • O153
[1] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969.
[2] VAN DAELE A. Multiplier Hopf algebras[J]. Transactions of the American Mathematical Society, 1994, 342(2):917-932.
[3] EL-HAFEZ A T A, DELVAUX L, VAN DAELE A. Group-cograded multiplier Hopf(*-)algebras[J]. Algebra and Representation Theory, 2007, 10(1):77-95.
[4] VIRELIZIER A. Hopf group-coalgebras[J]. Journal of Pure and Applied Algebra, 2002, 171(1):75-122.
[5] TURAEV V. Homotopy field theory in dimension 2 and group-algebras[J]. arXiv preprint math/9910010, 1999.
[6] LONG F W. The Brauer group of dimodule algebras[J]. Journal of Algebra, 1974, 30(1):559-601.
[7] MILITARU G. The Long dimodule category and nonlinear equation[J]. Algebra and Representation Theory, 1999, 2:177-200.
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