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Monomial Hopf algebras over fields of positive characteristic

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Abstract

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra C d (n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on C d (n) are completely classified. Moreover, we construct a Hopf algebras filtration on C d (n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

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References

  1. Chen, X. W., Huang, H. L., Ye, Y., Zhang, P., Monomial Hopf algebras, J. Algebra, 2004, 275: 212–232.

    Article  MathSciNet  Google Scholar 

  2. Cibils, C., Rosso, M., Hopf quivers, J. Algebra, 2002, 254(2): 241–251.

    Article  MathSciNet  Google Scholar 

  3. Green, E., Solberg, Ø., Basic Hopf algebras and quantum groups, Math. Z., 1998, 229: 45–76.

    Article  MathSciNet  Google Scholar 

  4. Montgomery, S., Indecomposable coalgebras, simple comodules and pointed Hopf algebras, Proc. AMS., 1995, 123: 2343–2351.

    MATH  Google Scholar 

  5. Auslander, M., Reiten, I., Smal, Ø., Representation Theory of Artin Algebras, Cambridge: Cambridge University Press, 1995, 30–35.

    Google Scholar 

  6. Kassel, C., Quantum Groups., New York: Springer-Verlag, 1995, 74–75.

    Google Scholar 

  7. Andruskiewitsch, N., Schneider, H.-J., Pointed Hopf algebras, in New Direction in Hopf Algebras (eds. Montgomery, S., Schneider, H-J.,), Math. Sci. Res. Inst. Publ. 43, Cambridge: Cambridge University Press, 2002, 1–68.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Liu Gongxiang

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Ye Yu

Authors
  1. Liu Gongxiang
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  2. Ye Yu
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Correspondence to Ye Yu.

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Liu, G., Ye, Y. Monomial Hopf algebras over fields of positive characteristic. SCI CHINA SER A 49, 320–329 (2006). https://doi.org/10.1007/s11425-006-0320-5

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  • DOI: https://doi.org/10.1007/s11425-006-0320-5

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