Skip to main content
Log in

Über das Synthese-Problem für nilpotente Liesche Gruppen

  • 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.

Literatur

  1. Boidol, J., Leptin, H., Schürmann, J., Vahle, D.: Räume primitiver Ideale von Gruppenalgebren. Math. Ann.236, 1–13 (1978)

    Google Scholar 

  2. Borel, A.: Linear algebraic groups. Amsterdam, New York: Benjamin 1969

    Google Scholar 

  3. Borho, W., Gabriel, P., Rentschler, R.: Primideale in Einhüllenden auflösbarer Lie-Algebren. Lecture Notes in Mathematics, Vol. 357. Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  4. Brown, I.D.: Dual topology of a nilpotent Lie group. Ann. Sci. École. Norm. Sup.6, 407–411 (1973)

    Google Scholar 

  5. Chevalley, C.: A new kind of relationship between matrices. Am. J. Math.65, 521–531 (1943)

    Google Scholar 

  6. Chevalley, C., Tuan, H.F.: On algebraic Lie algebras. Proc. Nat. Acad. Sci.31, 195–196 (1945)

    Google Scholar 

  7. Conze-Berline, N.: Espace des idéaux primitifs de l'algèbre enveloppante d'une algèbre de Lic nilpotente, J. Algebra34, 444–450 (1975)

    Google Scholar 

  8. Dixmier, J.: Opérateurs de rang fini dans les représentations unitaires. Publ. math. I. H. E. S.6, 305–317 (1960)

    Google Scholar 

  9. Dixmier, J.: Algèbres enveloppantes. Paris: Gauthier-Villiars 1974

    Google Scholar 

  10. Dixmier, J.: Idéaux, primitifs dans les algèbres enveloppantes. J. Algebra48, 96–112 (1977)

    Google Scholar 

  11. Duflo, M.: Sur les extensions des représentations irréductibles des groupes de Lie nilpotents. Ann. Sci. École Norm. Sup.5, 71–120 (1972)

    Google Scholar 

  12. Gurevich, D.J.: Counterexamples to a problem of L. Schwartz. Funct. Anal. Appl.9, 116–120 (1975)

    Google Scholar 

  13. Howe, R.E.: On the character of Weil's representation. Trans. Am. Math. Soc.177, 287–298 (1973)

    Google Scholar 

  14. Howe, R.E.: On a connection between nilpotent groups and oscillatory integrals associated to singularities. Pac. J. Math.73, 329–363 (1977)

    Google Scholar 

  15. Humphreys, J.E.: Linear algebraic groups. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  16. Jacobson, N.: Structure of rings, third edition. Am. Math. Soc. Coll. Publ.37 (1968)

  17. Kirillov, A.A.: Unitary representations of nilpotent Lie groups. Usp. Mat. Nauk17, 57–110 (1962)

    Google Scholar 

  18. Krisch, W., Müller, D.: On the synthesis problem for orbits of Lie groups in ℙn. Ark. Mat.18, 145–155 (1980)

    Google Scholar 

  19. Leptin, H.: Ideal theory in group algebras of locally compact groups. Invent. math.31, 259–278 (1976)

    Google Scholar 

  20. Ludwig, J.: Polynomial growth and ideals in group algebras. Manuscripta Math.30, 215–221 (1980)

    Google Scholar 

  21. Ludwig, J.: On the spectral synthesis problem for points in the dual of a nilpotent Lie group. Ark. Mat.21, 127–144 (1983)

    Google Scholar 

  22. Ludwig, J.: On primary ideals in the group algebra of a nilpotent Lie group. Math. Ann.262, 287–304 (1983)

    Google Scholar 

  23. Malgrange, B.: Existence et approximation de solutions des équations aux dérivées partielles et équations de convolutions. Ann. Inst. Fourier6, 271–355 (1956)

    Google Scholar 

  24. Matsushima, Y.: On algebraic Lie groups and algebras. J. Math. Soc. Japan1, 46–57 (1948)

    Google Scholar 

  25. Müller, D.: On the spectral synthesis problem for hypersurfaces of ℙn. J. Funct. Anal.47, 247–280 (1982)

    Google Scholar 

  26. Poguntke, D.: Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren. Math. Ann.227, 51–59 (1977)

    Google Scholar 

  27. Poguntke, D.: Algebraically irreducible representations of exponential Lie groups. Duke Math. J.50, 1077–1106 (1983)

    Google Scholar 

  28. Pukanszky, L.: Leçons sur les représentations des groupes Paris: Dunod 1967

    Google Scholar 

  29. Schwartz, L.: Théorie générale des fonctions moyenne-périodiques. Ann. Math.48, 857–929 (1947)

    Google Scholar 

  30. Schwartz, L.: Analyse et synthése harmonique dans les espaces de distributions. Canad. J. Math.3, 503–512 (1951)

    Google Scholar 

  31. Schwartz, L.: Théorie des distributions. 3èmeédit. Paris: Hermann 1973

    Google Scholar 

  32. Warner, G.: Harmonic analysis on semi-simple Lie groups, Vol. I. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Poguntke, D. Über das Synthese-Problem für nilpotente Liesche Gruppen. Math. Ann. 269, 431–467 (1984). https://doi.org/10.1007/BF01450760

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450760

Navigation