Skip to main content
Log in

Über die Gelfand-Kirillov-Dimension

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

Schrifttum

  1. Bernstein, I. N.: Dimension of commutative subrings inR n,k. Funkcional. Anal. i Prilozen.1, 79–81 (1967)

    Google Scholar 

  2. Borho, W., Gabriel, P., Rentschler, R.: Primideale in Einhüllenden auflösbarer Lie Algebren. Springer LN357 (1973)

  3. Borho, W., Rentschler, R.: Oresche Teilmengen in Einhüllenden Algebren. Math. Ann.217, 201–210 (1975)

    Google Scholar 

  4. Borho, W.: Primitive vollprime Ideale in der Einhüllenden von\(\mathfrak{s}\mathfrak{o}\)(5, ℂ). J. of Algebra (erscheint demnächst)

  5. Borho, W.: Berechnung der Gelfand-Kirillov-Dimension bei induzierten Darstellungen. Math. Ann. (erscheint demnächst)

  6. Bourbaki, N.: Algèbre commutative, Chapters III and IV. Paris: Hermann 1961

    Google Scholar 

  7. Cohn, P. M.: Skew field constructions. Carleton Math. Lecture Notes7 (1973)

  8. Conze, N., Dixmier, J.: Idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semisimple. Bull. Soc. math. 20,96, 339–351 (1972)

    Google Scholar 

  9. Conze, N.: Algèbres d'opérateurs différentiels et quotients des algèbres enveloppantes; Bull. Soc. math. France102, 379–415 (1974)

    Google Scholar 

  10. Demazure, M., Gabriel, P.: Groupes algébriques. I. Paris: Masson & Cie., Amsterdam: North-Holland 1970

    Google Scholar 

  11. Dixmier, J.: Algèbres enveloppantes. Paris: Gauthier-Villars 1974

    Google Scholar 

  12. Dixmier, J.: Idéaux primitifs dans l'algèbre enveloppante d'une algèbre de Lie semi-simple complex. C. R. Acad. Sci. Paris271, 134–136 (1970)

    Google Scholar 

  13. Dixmier, J.: Idéaux primitifs complètement premiers dans l'algèbre enveloppante de\(\mathfrak{s}\mathfrak{l}\) (3, ℂ). Colloque sur l'analyse harmonique non commutative. Springer LN466 (1975)

  14. Dixmier, J.: Primitive completely prime ideals in the enveloping algebra of\(\mathfrak{s}\mathfrak{l}_\mathfrak{n} \). (Tagungsberichte Oberwolfach 1975)

  15. Dynkin, E. B.: Semisimple subalgebras of semisimple Lie algebras. AMS Translations6, 111–244 (1957)

    Google Scholar 

  16. Gabriel, P., Rentschler, R.: Sur la dimension des anneaux et ensembles ordonnées. C. R. Acad. Sci.265, 712–715 (1967)

    Google Scholar 

  17. Gelfand, I. M., Kirillov, A. A.: Sur les corps liés aux algèbres enveloppantes des algèbres de Lie. Pub. IHES31, 5–19 (1966)

    Google Scholar 

  18. Gelfand, I. M., Kirillov, A. A.: Fields associated with enveloping algebras of Lie algebras. Doklady167, 407–409 (1966)

    Google Scholar 

  19. Govorov, V. E.: Graded algebras. Matem. Zametki12, 197–204 (1972)

    Google Scholar 

  20. Govorov, V. E.: On the dimension of graded algebras. Matem. Zametki14, 209–216 (1973)

    Google Scholar 

  21. Herstein, I. N.: Noncommutative rings. Menasha: John Wiley 1968

    Google Scholar 

  22. Jategaonkar, A. V.: Ore domains and free algebras. Bull. London Math. Soc.1, 45–46 (1969)

    Google Scholar 

  23. Joseph, A.: Sur les algèbres de Weyl (Vorlesungsausarbeitung 1974)

  24. Joseph, A.: Gelfand-Kirillov-dimension for algebras associated with Weyl algebras. Ann. Inst. Poincaré17, 325–336 (1972)

    Google Scholar 

  25. Joseph, A.: A generalisation of the Gelfand-Kirillov conjecture (erscheint demnächst)

  26. Joseph, A.: Minimal realizations and spectrum generating algebras. Comm. math. Phys.36, 325–338 (1974)

    Google Scholar 

  27. Joseph, A.: The minimal orbit of a simple Lie algebra and its associated maximal ideal (Tagungsberichte Oberwolfach 1975)

  28. Koševoi, E. G.: On certain associative algebras with transcendental relations. Algebra i Logika9, 520–529 (1970)

    Google Scholar 

  29. Kostant, B.: Lie group representations on polynomial rings. Am. J. Math.85, 327–404 (1963)

    Google Scholar 

  30. Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Am. J. Math.81, 973–1032 (1959)

    Google Scholar 

  31. Mazet, E.: Sur les travaux de Milnor-Wolf; Séminaire Berger: Variétés à courbure négative. Université Paris VII, 1970/71

  32. Milnor, J.: A note on curvature and fundamental groups; J. of Diff. Geom.2, 1–7 (1968)

    Google Scholar 

  33. Serre, J.-P.: Corps locaux. Paris: Hermann 1962

    Google Scholar 

  34. Wolf, J. A.: Growth of finitely generated solvable groups and curvature of Riemannian manifolds. J. of Diff. Geom.2, 421–446 (1968)

    Google Scholar 

  35. Bourbaki, N.: Groupes et algèbres de Lie. Paris: Hermann 1968

    Google Scholar 

  36. Joseph, A.: Second commutant theorems in the enveloping algebra of a Lie algebra (Vortrags-berichte Oberwolfach 1975)

  37. Bala, P., Carter, R. W.: The classification of unipotent and nilpotent elements. Indag. Math.36, 94–97 (1974)

    Google Scholar 

  38. Tits, J.: Free subgroups in linear groups. J. of Algebra20, 250–270 (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Bemerkung. Die Autoren möchten G. Harder, A. Joseph, M. Krämer und C. M. Ringel für hilfreiche Hinweise und Diskussionen danken.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borho, W., Kraft, H. Über die Gelfand-Kirillov-Dimension. Math. Ann. 220, 1–24 (1976). https://doi.org/10.1007/BF01354525

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01354525

Navigation