Skip to main content
SpringerLink
Log in

Quantum Lines for Dual Quasi-Bialgebras

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

In this paper, the theory to construct quantum lines for general dual quasi-bialgebras is developed followed by some specific examples where the dual quasi-bialgebras are pointed with cyclic group of points.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Angiono, I.E. : Basic quasi-Hopf algebras over cyclic groups. Adv. Math. 225, 3545–3575 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ardizzoni, A., Pavarin, A.: Bosonization for dual quasi-bialgebras and preantipode. J. Algebra 390, 126–159 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Călinescu, C., Dǎscǎlescu, S., Masuoka, A., Menini, C.: Quantum lines over non-cocommutative cosemisimple Hopf algebras. J. Algebra 273(2), 753–779 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Etingof, P., Gelaki, S.: Finite-dimensional quasi-Hopf algebras with radical of codimension 2. Math. Res. Lett. 11, 685–696 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Etingof, P., Gelaki, S.: On radically graded finite-dimensional quasi-Hopf algebras. Mosc. Math. J 5(2), 371–378 (2005)

    MATH  MathSciNet  Google Scholar 

  6. Etingof, P., Gelaki, S.: Liftings of graded quasi-Hopf algebras with radical of prime codimension. J. Pure Appl. Algebra 205(2), 310–322 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gelaki, S.: Basic quasi-Hopf algebras of dimension n 3. J. Pure Appl. Algebra 198(1-3), 165–174 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kassel, C.: Quantum groupsGraduate Text in Mathematics, Vol. 155. Springer (1995)

  9. Mac Lane, S.: Categories for the working mathematician. Second editionGraduate Texts in Mathematics, Vol. 5. Springer-Verlag, New York (1998)

  10. Moore, G., Seiberg, N.: Classical and quantum conformal field theory. Comm. Math. Phys. 123(2), 177–254 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schauenburg, P.: Quotients of finite quasi-Hopf algebras. Hopf algebras in noncommutative geometry and physics, Vol. 239, pp 281–290. Dekker, New York (2005)

    Google Scholar 

  12. Sweedler, M.E.: Cohomology of algebras over Hopf algebras. Trans. Amer. Math. Soc. 133, 205–239 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  13. Sweedler, M.: Hopf Algebras. Benjamin, New York (1969)

    Google Scholar 

  14. Takeuchi, M.: Free Hopf algebras generated by coalgebras. J. Math. Soc. Japan 23, 561–582 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  15. Weibel, C.: An introduction to homological algebraCambridge Studies in Advanced Mathematics, Vol. 38. Cambridge University Press, Cambridge (1994)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 35, Ferrara, I-44121, Italy

    Claudia Menini

  2. Department of Mathematics “G. Peano”, University of Turin, via Carlo Alberto 10, I-10123, Torino, Italy

    Alessandro Ardizzoni

  3. Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada, E4L 1E6

    Margaret Beattie

Authors
  1. Claudia Menini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alessandro Ardizzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Margaret Beattie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claudia Menini.

Additional information

This paper was written while A. Ardizzoni and C. Menini were members of GNSAGA. A. Ardizzoni was partially supported by the research grant “Progetti di Eccellenza 2011/2012” from the “Fondazione Cassa di Risparmio di Padova e Rovigo”. M. Beattie was supported by an NSERC Discovery Grant. Her stay, as a visiting professor at University of Ferrara in 2011, was supported by INdAM

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Menini, C., Ardizzoni, A. & Beattie, M. Quantum Lines for Dual Quasi-Bialgebras. Algebr Represent Theor 18, 35–64 (2015). https://doi.org/10.1007/s10468-014-9478-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10468-014-9478-7

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation