Skip to main content
SpringerLink
Log in

Harish-Chandra isomorphisms for quantum algebras

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The center of the quantum algebra is studied. Especially an analogue of the Harish-Chandra isomorphism is established.

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. Abe, E.: Hopf algebras. Cambridge, New York: Cambridge University Press 1980

    Google Scholar 

  2. Dixmier, J.: Algèbres Enveloppantes. Paris: Gauthier-Villars 1974

    Google Scholar 

  3. Drinfel'd V. G.: Hopf algebras and the quantum Yang-Baxter equation. Soviet Math. Dokl.32, 254–258 (1985)

    Google Scholar 

  4. Drinfel'd, V. G.: Quantum groups. In: Proc. ICM, Berkeley, 1986. Providence, RI: Am. Math. Soc., 1988

    Google Scholar 

  5. Harish-Chandra: On some applications of the universal enveloping algebra of a semisimple Lie algebra. Trans. Am. Math. Soc.70, 28–96 (1951)

    Google Scholar 

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

    Google Scholar 

  7. Jimbo, M.: Aq-analogue of U(gl(N+1)), Hecke algebras and the Yang-Baxter equation. Lett. Math. Phys.11, 247–252 (1986)

    Google Scholar 

  8. Kac, V. G.: Infinite dimensional Lie algebras. Progress in Math. Vol.44, Boston, MA: Birkhäuser 1983

    Google Scholar 

  9. Lusztig, G.: Quantum deformations of certain simple modules over enveloping algebras. Adv. Math.70, 237–249 (1988)

    Google Scholar 

  10. Matsumura, H.: Commutative algebra. Second ed. London: Benjamin 1980

    Google Scholar 

  11. Rosso, M.: Finite dimensional representations of the quantum analog of a complex simple Lie algebra. Commun. Math. Phys.117, 581–593 (1988)

    Google Scholar 

  12. Serre, J. P.: Algèbres de Lie semi-simples complexes. New York: Benjamin 1966

    Google Scholar 

  13. Yamane, H.: A Poincaré-Birkhoff-Witt theorem for quantized universal enveloping algebras of typeA N, preprint

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of General Education, Osaka University, 560, Toyonaka, Japan

    Toshiyuki Tanisaki

Authors
  1. Toshiyuki Tanisaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicted by H. Araki

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tanisaki, T. Harish-Chandra isomorphisms for quantum algebras. Commun.Math. Phys. 127, 555–571 (1990). https://doi.org/10.1007/BF02104501

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02104501

Keywords

Search

Navigation