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Yetter-Drinfeld modules over the Hopf-Ore extension of the group algebra of dihedral group

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Abstract

Let k be an algebraically closed field of characteristic zero, and D n be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD n . We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0).

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References

  1. Yetter, D. N.: Quantum groups and representations of monoidal categories. Math. Proc. Cambridge Philos. Soc., 108, 261–290 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kassel, C.: Quantum Groups, Springer, New York, 1995

    Book  MATH  Google Scholar 

  3. Montgomery, S.: Hopf Algebras and Their Actions on Rings, CBMS Ser. Math., Vol. 82, Amer. Math. Soc., 1993

  4. Beattie, M., Dascalescu, S., Grunenfelder, L.: Constructing pointed Hopf algebras by Ore extensions. J. Algebra, 225, 743–770 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Beattie, M.: An isomorphism theorem for Ore extension Hopf algebras. Comm. Algebra, 28, 569–584 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Panov, A. N.: Ore extensions of Hopf algebras. Math. Notes, 74(3), 401–410 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wang, Z.: Simple modules over the Hopf Ore extension of the Dihedral group (in Chinese). J. Zhejiang Normal University, 31(4), 377–381 (2008)

    MATH  Google Scholar 

  8. Sweedler, M. E.: Hopf Algebra, Benjamin, New York, 1969

    Google Scholar 

  9. Chen, H. X., Zhang, Y.: Four-dimensional Yetter-Drinfeld module algebras. J. Algebra, 296, 582–634 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Radford, D. E.: On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra. J. Algebra, 270, 670–695 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Information Science, School of Mathematical and Physical, Changzhou University, Changzhou, 213164, P. R. China

    Hong Zhu

  2. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, P. R. China

    Hong Zhu & Hui Xiang Chen

Authors
  1. Hong Zhu
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  2. Hui Xiang Chen
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Correspondence to Hong Zhu.

Additional information

Supported by NSF of China (Grant No. 11171291) and Doctorate Foundation (Grant No. 200811170001), Ministry of Education of China

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Zhu, H., Chen, H.X. Yetter-Drinfeld modules over the Hopf-Ore extension of the group algebra of dihedral group. Acta. Math. Sin.-English Ser. 28, 487–502 (2012). https://doi.org/10.1007/s10114-011-9777-4

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  • DOI: https://doi.org/10.1007/s10114-011-9777-4

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