Skip to main content
Log in

Quantum groups at roots of 1

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We extend to the not necessarily simply laced case the study [8] of quantum groups whose parameter is a root of 1.

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. Chevalley, C., ‘Certains schémas de groupes semisimples’, Séminaire Bourbaki (1961/62).

  2. Drinfeld, V. G., ‘Hopf algebras and the Yang-Baxter equation’, Soviet Math. Dokl. 32 (1985), 254–258.

    Google Scholar 

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

    Google Scholar 

  4. Kostant, B., ‘Groups over Z’, Proc. Symp. Pure Math. 9 (1966), 90–98.

    Google Scholar 

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

    Google Scholar 

  6. Lusztig, G., ‘Modular representations and quantum groups’, Contemp. Math. 82 (1989), 59–77.

    Google Scholar 

  7. Lusztig, G., ‘On quantum groups’, J. of Algebra 128 (1990).

  8. Lusztig, G., ‘Finite dimensional Hopf algebras arising from quantum groups’, J. Amer. Math. Soc. 3 (1990).

  9. Rosso, M., ‘Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra’, Comm. Math. Phys. 117 (1988), 581–593.

    Google Scholar 

  10. Rosso, M., ‘Analogues de la forme de Killing et du théorème d'Harish-Chandra pour les groupes quantiques’, Preprint.

  11. Steinberg, R., Lectures on Chevalley Groups (in Russian), Mir, Moscow, 1975.

    Google Scholar 

  12. Tanisaki, T., ‘Finite dimensional representations of quantum groups’, Preprint.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Jacques Tits on his sixtieth birthday

Supported in part by National Science Foundation Grant DMS 8702842.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lusztig, G. Quantum groups at roots of 1. Geom Dedicata 35, 89–113 (1990). https://doi.org/10.1007/BF00147341

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00147341

Keywords

Navigation