Skip to main content
SpringerLink
Log in

Mathematical guide to quantum groups

  • I. Structure of Quantum Groups
  • Conference paper
  • First Online:
Quantum Groups

Part of the book series: Lecture Notes in Physics ((LNP,volume 370))

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abe, E.Hopf Algebras. University Press, Cambridge, 1980.

    Google Scholar 

  2. Bayen, F., Plato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D. Deformation theory and quantization. I. Deformations of symplectic structures. Ann. Phys. 111 (1978), 61–110.

    Google Scholar 

  3. Bayen, F., Plato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D. Deformation theory and quantization. II. Physical applications. Ann. Phys. 111 (1978), 111–151.

    Google Scholar 

  4. Drinfel'd, V. G. Hamitonian structures on Lie groups, Lie bialgebras and the geometric meaning of the classical Yang-Baxter equations. Soviet Math. Dokl. 27 (1983), 68–71.

    Google Scholar 

  5. Drinfel'd, V. G.Quantum Groups, vol. 1 of Proceedings of the International Congress of Mathematicians, Berkeley, California, USA, 1986. Academic Press, 1987, pp. 798–820.

    Google Scholar 

  6. Grothendieck. Résumé des résultats essentiels dans la théorie des produits tensoriels topologiques et des espaces nucléaires. Ann. Inst. Fourier 4 (1952), 73–112.

    Google Scholar 

  7. Helgason, S.Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, London, 1978.

    Google Scholar 

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

    Google Scholar 

  9. Kac, V. G.Infinite dimensional Lie algebras. Birkhäuser, Boston-Basel-Stuttgart, 1983.

    Google Scholar 

  10. Libermann, P., and Marls, C.-M.Symplectic Geometry and Analytical Mechanics. D. Reidel, Dordrecht, 1987.

    Google Scholar 

  11. Manin, Y. I. Quantum groups and non-commutative geometry. Preprint Montreal University CRM-1561 (1988).

    Google Scholar 

  12. Milnor, J. W., and Moors, J. C. On the structure of Hopf algebras. Ann. Math. 81 (1965), 211–264.

    Google Scholar 

  13. Schwartz, L.Théorie des distributions. Hermann, Paris, 1966.

    Google Scholar 

  14. Sklyanin, E. On an algebra generated by quadratic relations. Usp. Mathem. Nauk 40. (1985), 214.

    Google Scholar 

  15. Woronowicz, S. L. Compact matrix pseudogroups. Commun. Math. Phys. 111 (1987), 613–665.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Arnold Sommerfeld Institute for Mathematical Physics, TU Clausthal

    H. D. Doebner, J. D. Hennig & W. Lücke

Authors
  1. H. D. Doebner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. D. Hennig
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Lücke
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

H. -D. Doebner J. -D. Hennig

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this paper

Cite this paper

Doebner, H.D., Hennig, J.D., Lücke, W. (1990). Mathematical guide to quantum groups. In: Doebner, H.D., Hennig, J.D. (eds) Quantum Groups. Lecture Notes in Physics, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53503-9_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-53503-9_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53503-4

  • Online ISBN: 978-3-540-46647-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation