Skip to main content
Log in

Quantum Weyl symmetric polynomials and the center of quantum group U q (sl4)

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group U q (sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alev J, Dumas F. Sur le corps des fractions de certaines alg bres quantiques. J Algebra, 1994, 170: 229–265

    Article  MATH  MathSciNet  Google Scholar 

  2. Baumann P. On the centers of quantized enveloping algebras. J Algebra, 1998, 203: 244–260

    Article  MATH  MathSciNet  Google Scholar 

  3. Caldero P. On the q-commutations in U q(n). J Algebra, 1998, 210: 557–576

    Article  MATH  MathSciNet  Google Scholar 

  4. Caldero P. On harmonic elements for semi-simple Lie algebras. Adv Math, 2002, 166: 73–99

    Article  MATH  MathSciNet  Google Scholar 

  5. Dixmier J. Enveloping Algebras. Grad Stud Math, vol. II. Providence, RI: Amer Math Soc, 1996

    Google Scholar 

  6. Drinfel’d V G. Hopf algebras and quantum Yang-Baxter equation. Soviet Math Dokl, 1985, 32: 254–258

    Google Scholar 

  7. Drinfel’d V G. Quantum Groups. Berkeley: Proc ICM, 1986, 798–820

    Google Scholar 

  8. Gauger M A. Some remarks on the center of the universal enveloping algebra of a classical simple Lie algebra. Pacific J Math, 1976, 62: 93–97

    MATH  MathSciNet  Google Scholar 

  9. Farkas D R. Multiplicative invariants. Enseign Math, 1984, 30: l41–157

    MathSciNet  Google Scholar 

  10. Humphreys J E. Introduction to Lie algebras and their representation theory. Grad Stud Math, vol. 9. New York: Springer-Verlag, 1972

    Google Scholar 

  11. Jantzen J C. Lecture on quantum groups. Grad Stud Math, vol. 6. Providence, RI: Amer Math Soc, 1996

    Google Scholar 

  12. Jimbo M. A q-difference analogue of U(g) and the Yang-Baxter equation. Lett Math Phys, 1985, 10: 63–69

    Article  MATH  MathSciNet  Google Scholar 

  13. Joseph A. Quantum groups and their primitive ideals. Ergenbnisse der Mathematik und ihrer Grenzgebiete. vol. 29. New York: Springer-Verlag, 1995

    Google Scholar 

  14. Kassel C. Quantum Groups. Berlin-Heidelberg-New York: Springer, 1995

    MATH  Google Scholar 

  15. Lachowska A. On the center of the small quantum group. J Algebra, 2003, 262: 313–331

    Article  MATH  MathSciNet  Google Scholar 

  16. Lorenz M. Multiplicative Invariant Theory. Berlin-Heidelberg-New York: Springer, 2006

    Google Scholar 

  17. Li L B, Wu J Y, Pan Y. Quantum Weyl polynomials and the center of quantum group U q(sl3). Algebra Colloq, to appear

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to LiBin Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, J., Wei, J. & Li, L. Quantum Weyl symmetric polynomials and the center of quantum group U q (sl4). Sci. China Math. 54, 55–64 (2011). https://doi.org/10.1007/s11425-010-4125-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-010-4125-1

Keywords

MSC(2000)

Navigation