Minimal C*-dense ideals and algebraically irreducible representations of the schwartz-algebra of a nilpotent lie group

J. Boidol, H. Leptin, J. Schürmann, D. Vahle, Räume primitiver Ideale in Gruppenalgebren, Math. Ann. 236 (1978), 1–13.
Article MathSciNet MATH Google Scholar
I.D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. Ec. Norm. Sup. 6 Sér. 4 (1973), 407–411.
MathSciNet MATH Google Scholar
J. Dixmier, Opérateurs de rang fini dans les représentations unitaires, Publ. Math. IHES 6 (1960), 305–317.
MathSciNet MATH Google Scholar
J. Dixmier, Les C*-Algèbres et leurs représentations, Gauthier-Villars.
Google Scholar
J. Dixmier, P. Malliavin, Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. (2) 102 (1978), 305–330.
MathSciNet MATH Google Scholar
F. Du Cloux, Représentations temperées des groupes de Lie nilpotents, Preprint (1987).
Google Scholar
F. Du Cloux, Jets de fonctions différentiables sur le dual d'un groupe de Lie nilpotent, Invent. Math. 88 (1987), 375–394.
Article MathSciNet MATH Google Scholar
F.F. Bonsall, J. Duncan, Complete normed algebras, Springer-Verlag, Berlin-Heidelberg-New York (1973).
Book MATH Google Scholar
R. Howe, On a connection between nilpotent groups and oscillatory integrals associated to singularities, Pac. J. Math. 73 (1977), n. 2, 329–363.
Article MathSciNet MATH Google Scholar
A. Hulanicki, A functional calculus for Rockland operators on nilpotent Lie groups. Stud. Math. 78 (1974), 253–266.
MathSciNet MATH Google Scholar
N. Jacobson, Structure of rings, third edition, Amer. Math. Soc. Coll. Publ. 37 (Providence 1968).
Google Scholar
A.A. Kirillov, Unitary representations of nilpotent Lie groups, Usp. Mat. Nauk 17 (1962), 57–110.
MathSciNet MATH Google Scholar
J. Ludwig, On primary ideals in the group algebra of a nilpotent Lie group, Math. Ann. 262 (1983), 287–304.
Article MathSciNet MATH Google Scholar
J. Ludwig, A class of symmetric and a class of Wiener group algebras, J. Funct. Annal. 31, (1979), 187–194.
Article MathSciNet MATH Google Scholar
J. Ludwig, The element of bounded trace in the C*-algebra of a nilpotent Lie group, Invent. math. 83 (1986), 167–190.
Article MathSciNet MATH Google Scholar
T. Pytlik, On the spectral radius of elements in groups algebras, Bull. Acad. Polon. Sci. 21 (1973), 899–902.
MathSciNet MATH Google Scholar

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Séminaire de Mathématique, Centre Universitaire, 162 A, Avenue de la Faïencerie, L-1511, Luxembourg
Jean Ludwig

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Pierre Eymard Jean-Paul Pier

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Ludwig, J. (1988). Minimal C*-dense ideals and algebraically irreducible representations of the schwartz-algebra of a nilpotent lie group. In: Eymard, P., Pier, JP. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086601

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DOI: https://doi.org/10.1007/BFb0086601
Published: 02 October 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50524-2
Online ISBN: 978-3-540-46032-9
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Minimal C*-dense ideals and algebraically irreducible representations of the schwartz-algebra of a nilpotent lie group

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