Skip to main content
SpringerLink
Log in

Dual Algebras of Some Semisimple Finite-dimensional Hopf Algebras

  • Conference paper
Modules and Comodules

Part of the book series: Trends in Mathematics ((TM))

Abstract

In this paper we establish properties of dual Hopf algebras for two series of finite-dimensional semisimple Hopf algebras. It is shown none of dual algebra belong to this class.

Research partially supported by grants RFBR 06-01-00037, NSh-5666.2006.1.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Artamonov V.A. On semisimple finite dimensional Hopf algebras, Math. Sbornik (to appear).

    Google Scholar 

  2. Artamonov V.A., Slovokhotov Yu.L. Group theory and their applications in physics, chemistry and crystallography, Publishing center “Academia”, Moscow, 2005.

    Google Scholar 

  3. Bourbaki N., Algebra, Ch. IX. Paris, Hermann.

    Google Scholar 

  4. Bahturin Y.A., Zaicev M.V., Group gradings on associative algebras, J. Algebra, 241(2001), 677–698.

    Article  MATH  MathSciNet  Google Scholar 

  5. Curtis Ch.W., Reiner I. Representation theory of finite groups and associative algebras. Interscience Publ., Witney & Sons, New York, London, 1962.

    MATH  Google Scholar 

  6. Jiang-Hua Lu, Min Yanm, Youngchang Zhu, Quasi-triangular structure on Hopf algebras with positive bases. Contemp. Math., 267(2000), 339–356.

    Google Scholar 

  7. Huppert B., Character theory of finite groups, de Gruyter Expositions in Mathematics 25, 1998.

    Google Scholar 

  8. Kac, G., Paljutkin, V., Finite ring groups, Trudy Moscow Math. Obschestva, 15 (1966), 224–261.

    MathSciNet  Google Scholar 

  9. Larson, R., Radford, D., Finite-dimensional cosemisimple Hopf algebras in characteristic zero are semisimple. J. Algebra, 117(1988), 267–289.

    Article  MATH  MathSciNet  Google Scholar 

  10. Montgomery, S., Hopf Algebras and Their Actions on Rings, Regional Conf. Ser. Math. Amer. Math. Soc., Providence RI, 1993.

    Google Scholar 

  11. Montgomery S., Classifying finite-dimensional semisimple Hopf algebras, Contemp. Math., 229(1998), 265–279.

    Google Scholar 

  12. Natale S., On group theoretical algebras and exact factorizations of finite groups, J. Algebra, 270 (2003), 190–211.

    Article  MathSciNet  Google Scholar 

  13. Natale S., Semisolvability of semisimple Hopf algebras of low dimension, Memoirs of AMS vol. 186, 2007.

    Google Scholar 

  14. Nichols W., Zoeller M., A Hopf algebra freeness theorem, Amer. J. Math., 111(1989), 381–385.

    Article  MATH  MathSciNet  Google Scholar 

  15. O’Meara O.T., Symplectic groups, Providence RI, Amer. Math. Soc., 1978.

    Google Scholar 

  16. Pierce, R.S., Associative algebras, Springer-Verlag, New York, Heidelberg, Berlin, 1982.

    MATH  Google Scholar 

  17. Schneider H.-J., Lectures on Hopf algebras, Universidad de Cordoba, Trabajos de Matematica, N 31/95, Cordoba (Argentina), 1995.

    Google Scholar 

  18. Seitz G.M., Finite groups having only one irreducible representation of degree greater than one. Proc. Amer. Math. Soc. 19(1968), 459–461.

    Article  MATH  MathSciNet  Google Scholar 

  19. Tambara D., Representations of tensor categories with fusion rules of self-duality for finite abelian groups, Israel J. Math., 118(2000), 29–60.

    Article  MATH  MathSciNet  Google Scholar 

  20. Tambara D., Yamagami S., Tensor categories with fusion rules of self-duality for finite abelian groups, J.Algebra 209(1998), 692–707.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Algebra Faculty of Mechanics and Mathematics, Moscow State University, Moscow

    V. A. Artamonov & I. A. Chubarov

Authors
  1. V. A. Artamonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Chubarov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, UK

    Tomasz Brzeziński

  2. Departamento de Alxebra, Universidade de Santiago, 15782, Santiago de Compostela, Spain

    José Luis Gómez Pardo

  3. Instituto de Matemática e Estatística da, Universidade de São Paulo (IME-USP), Rua do Matão, 1010 Cidade Universitária, CEP 05508-090, São Paulo - SP, Brasil

    Ivan Shestakov

  4. Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, Scotland,UK

    Patrick F. Smith

Additional information

To Prof. Robert Wisbauer on the occasion of his 65th anniversary

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Artamonov, V.A., Chubarov, I.A. (2008). Dual Algebras of Some Semisimple Finite-dimensional Hopf Algebras. In: Brzeziński, T., Gómez Pardo, J.L., Shestakov, I., Smith, P.F. (eds) Modules and Comodules. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8742-6_4

Download citation

Publish with us

Policies and ethics

Search

Navigation