Duke Mathematical Journal

Algebraically irreducible representations of $L^1$-algebras of exponential Lie groups

Detlev Poguntke
Source: Duke Math. J. Volume 50, Number 4 (1983), 1077-1106.
First Page: Show Hide
Primary Subjects: 22E27
Secondary Subjects: 22E25
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077303490
Mathematical Reviews number (MathSciNet): MR726318
Zentralblatt MATH identifier: 0555.43005
Digital Object Identifier: doi:10.1215/S0012-7094-83-05045-7

References

[1] P. Bernat, N. Conze, M. Duflo, M. Lévy-Nahas, M. Raïs, P. Renouard, and M. Vergne, Représentations des groupes de Lie résolubles, Dunod, Paris, 1972.
Mathematical Reviews (MathSciNet): MR56:3183
Zentralblatt MATH: 0248.22012
[2] J. Boidol, H. Leptin, J. Schürman, and D. Vahle, Räume primitiver Ideale von Gruppenalgebren, Math. Ann. 236 (1978), no. 1, 1–13.
Mathematical Reviews (MathSciNet): MR58:16959
Zentralblatt MATH: 0363.46057
Digital Object Identifier: doi:10.1007/BF01420252
[3] J. Boidol, $\ast$-regularity of exponential Lie groups, Invent. Math. 56 (1980), no. 3, 231–238.
Mathematical Reviews (MathSciNet): MR81k:22005
Zentralblatt MATH: 0423.22008
Digital Object Identifier: doi:10.1007/BF01390046
[4] J. Boidol, Connected groups with polynomially induced dual, J. Reine Angew. Math. 331 (1982), 32–46.
Mathematical Reviews (MathSciNet): MR83i:22010
Zentralblatt MATH: 0471.22004
Digital Object Identifier: doi:10.1515/crll.1982.331.32
[5] F. F. Bonsall and J. Duncan, Complete normed algebras, Springer-Verlag, New York, 1973.
Mathematical Reviews (MathSciNet): MR54:11013
Zentralblatt MATH: 0271.46039
[6] I. D. Brown, Dual topology of a nilpotent Lie group, Ann. Sci. École Norm. Sup. (4) 6 (1973), 407–411.
Mathematical Reviews (MathSciNet): MR50:4813
Zentralblatt MATH: 0284.57026
[7] J. Dixmier, Opérateurs de rang fini dans les représentations unitaires, Inst. Hautes Études Sci. Publ. Math. (1960), no. 6, 13–25.
Mathematical Reviews (MathSciNet): MR25:149
Zentralblatt MATH: 0100.32303
Digital Object Identifier: doi:10.1007/BF02698776
[8] M. Duflo, Sur les extensions des représentations irréductibles des groupes de Lie nilpotents, Ann. Sci. École Norm. Sup. (4) 5 (1972), 71–120.
Mathematical Reviews (MathSciNet): MR46:1966
Zentralblatt MATH: 0241.22030
[9] J. M. G. Fell, The dual spaces of Banach algebras, Trans. Amer. Math. Soc. 114 (1965), 227–250.
Mathematical Reviews (MathSciNet): MR30:2357
Zentralblatt MATH: 0131.33102
Digital Object Identifier: doi:10.2307/1993999
[10] J. M. G. Fell, Non-unitary dual spaces of groups, Acta Math. 114 (1965), 267–310.
Mathematical Reviews (MathSciNet): MR32:4210
Zentralblatt MATH: 0152.33204
Digital Object Identifier: doi:10.1007/BF02391824
[11] R. E. Howe, On a connection between nilpotent groups and oscillatory integrals associated to singularities, Pacific J. Math. 73 (1977), no. 2, 329–363.
Mathematical Reviews (MathSciNet): MR58:28270
Zentralblatt MATH: 0383.22009
Project Euclid: euclid.pjm/1102810615
[12] N. Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37. Revised edition, American Mathematical Society, Providence, R.I., 1964.
Mathematical Reviews (MathSciNet): MR36:5158
Zentralblatt MATH: 0218.17010
[13] W. Kirsch and D. Müller, On the synthesis problem for orbits of Lie groups in $\bf R\spn$, Ark. Mat. 18 (1980), no. 2, 145–155.
Mathematical Reviews (MathSciNet): MR82f:43006
Zentralblatt MATH: 0478.43004
Digital Object Identifier: doi:10.1007/BF02384687
[14] M. Leinert, Beitrag zur Theorie der verallgemeinerten $\cal L\sp1$-Algebren, Arch. Math. (Basel) 21 (1970/71), 594–600.
Mathematical Reviews (MathSciNet): MR45:5776
Zentralblatt MATH: 0221.43009
Digital Object Identifier: doi:10.1007/BF01220971
[15] H. Leptin, Verallgemeinerte $L\sp1$-Algebren und projektive Darstellungen lokal kompakter Gruppen. I, II, Invent. Math. 3 (1967), 257-281; ibid. 4 (1967), 68–86.
Mathematical Reviews (MathSciNet): MR37:5328
Zentralblatt MATH: 0179.18303
Digital Object Identifier: doi:10.1007/BF01404580
[16] H. Leptin, Ideal theory in group algebras of locally compact groups, Invent. Math. 31 (1975/76), no. 3, 259–278.
Mathematical Reviews (MathSciNet): MR53:3189
Zentralblatt MATH: 0328.22012
Digital Object Identifier: doi:10.1007/BF01403147
[17] H. Leptin and D. Poguntke, Symmetry and nonsymmetry for locally compact groups, J. Funct. Anal. 33 (1979), no. 2, 119–134.
Mathematical Reviews (MathSciNet): MR81e:43010
Zentralblatt MATH: 0414.43004
Digital Object Identifier: doi:10.1016/0022-1236(79)90107-1
[18] J. Ludwig, Polynomial growth and ideals in group algebras, Manuscripta Math. 30 (1980), no. 3, 215–221.
Mathematical Reviews (MathSciNet): MR81e:43012
Zentralblatt MATH: 0417.43005
Digital Object Identifier: doi:10.1007/BF01303328
[19] J. Ludwig, On points in the dual of a nilpotent Lie group, submitted to Ark. Mat.
[20] J. Ludwig, On primary ideals in the group algebra of a nilpotent Lie group, to appear in Math. Ann.
Mathematical Reviews (MathSciNet): MR692858
Zentralblatt MATH: 0489.22009
Digital Object Identifier: doi:10.1007/BF01456011
[21] M. A. Naĭ mark, Normed algebras, Wolters-Noordhoff Publishing, Groningen, 1972.
Mathematical Reviews (MathSciNet): MR55:11042
[22] D. Poguntke, Nilpotente Liesche Gruppen haben symmetrische Gruppenalgebren, Math. Ann. 227 (1977), no. 1, 51–59.
Mathematical Reviews (MathSciNet): MR56:6283
Zentralblatt MATH: 0347.22005
Digital Object Identifier: doi:10.1007/BF01360962
[23] D. Poguntke, Symmetry (or simple modules) of some Banach algebras, Harmonic analysis, Iraklion 1978 (Proc. Conf., Univ. Crete, Iraklion, 1978), Lecture Notes in Math., vol. 781, Springer, Berlin, 1980, pp. 177–193.
Mathematical Reviews (MathSciNet): MR81e:43013
Zentralblatt MATH: 0429.46030
[24] D. Poguntke, Symmetry and nonsymmetry for a class of exponential Lie groups, J. Reine Angew. Math. 315 (1980), 127–138.
Mathematical Reviews (MathSciNet): MR82b:43013
Zentralblatt MATH: 0419.22014
Digital Object Identifier: doi:10.1515/crll.1980.315.127
[25] D. Poguntke, Einfache Moduln über gewissen Banachschen Algebren: ein Imprimitivitätssatz, Math. Ann. 259 (1982), no. 2, 245–258.
Mathematical Reviews (MathSciNet): MR84i:22008
Zentralblatt MATH: 0472.46038
Digital Object Identifier: doi:10.1007/BF01457311
[26] D. Poguntke, Operators of finite rank in unitary representations of exponential Lie groups, Math. Ann. 259 (1982), no. 3, 371–383.
Mathematical Reviews (MathSciNet): MR83i:22018
Zentralblatt MATH: 0471.22005
Digital Object Identifier: doi:10.1007/BF01456949
[27] D. Poguntke, Kunze–Stein phenomenon and $L^p$-estimates of matrix coefficients for a certain solvable Lie group, to appear in the Proceedings of the OAGR conference in Neptun (Roumania), Pitman Publ.: London, 1980.
Mathematical Reviews (MathSciNet): MR733305
Zentralblatt MATH: 0524.22011
[28] C. E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960.
Mathematical Reviews (MathSciNet): MR22:5903
Zentralblatt MATH: 0095.09702

2013 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?