Lie groups with smooth characters and with smooth semicharacters

Niels Vigand Pedersen

Compositio Mathematica (1983)

  • Volume: 48, Issue: 2, page 185-208
  • ISSN: 0010-437X

How to cite

top

Pedersen, Niels Vigand. "Lie groups with smooth characters and with smooth semicharacters." Compositio Mathematica 48.2 (1983): 185-208. <http://eudml.org/doc/89591>.

@article{Pedersen1983,
author = {Pedersen, Niels Vigand},
journal = {Compositio Mathematica},
keywords = {solvable; type R; characters; distributions; semicharacters; semifinite factor representation; normal representations},
language = {eng},
number = {2},
pages = {185-208},
publisher = {Martinus Nijhoff Publishers},
title = {Lie groups with smooth characters and with smooth semicharacters},
url = {http://eudml.org/doc/89591},
volume = {48},
year = {1983},
}

TY - JOUR
AU - Pedersen, Niels Vigand
TI - Lie groups with smooth characters and with smooth semicharacters
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 48
IS - 2
SP - 185
EP - 208
LA - eng
KW - solvable; type R; characters; distributions; semicharacters; semifinite factor representation; normal representations
UR - http://eudml.org/doc/89591
ER -

References

top
  1. [1] L. Auslander and C.C. Moore: Unitary representations of solvable Lie groups, Mem. Amer. Math. Soc.62, Providence, Rhode Island, 1966. Zbl0204.14202MR207910
  2. [2] P. Bernat et al.: Représenations des groupes de Lie résolubles, Dunod, Paris, 1972. Zbl0248.22012MR444836
  3. [3] N. Bourbaki: Intégration, Chap. VII-VIII: Convolution et représentations, Hermann, Paris, 1963. 
  4. [4] N. Bourbaki: Intégration, Chap. V: Intégration des mesures, 2ième éd., Hermann, Paris, 1967. Zbl0143.27101MR209424
  5. [5] C. Chevalley: Théorie des groupes de Lie, tome II: Groupes algébriques, Hermann, Paris, 1951. Zbl0054.01303MR51242
  6. [6] C. Chevalley: Théorie des groupes de Lie, tome III: Théorèmes généraux sur les algèbres de Lie, Hermann, Paris, 1955. Zbl0186.33104MR68552
  7. [7] J. Dixmier: Sur les représentations unitaires des groupes de Lie nilpotents. V, Bull. Soc. Math. France87 (1959), 65-79. Zbl0152.01302MR115097
  8. [8] J. Dixmier: Les algèbres d'opérateurs dans l'expace Hilbertien, 2ième éd., Gauthier-Villars, Paris, 1969. Zbl0175.43801
  9. [9] J. Dixmier: Les C*-algèbres et leurs représentations, 2 ième éd., Gauthier-Villars, Paris, 1969. Zbl0174.18601MR246136
  10. [10] J. Dixmier: Sur la représentation régulière d'un groupe localement compact connexe, Ann. Sci. École Norm. Sup. (4) 2 (1969), 423-436. Zbl0186.46304MR260933
  11. [11] E.G. Effros: A decomposition theory for representations of C*-algebras, Trans. Amer. Math. Soc., 107 (1963), 83-106. Zbl0113.09602MR146682
  12. [12] J. Glimm: Locally compact transformation groups, Trans. Amer. Math. Soc.101 (1961), 124-138. Zbl0119.10802MR136681
  13. [13] Harish- Chandra: Representations of semisimple Lie groups. III, Trans. Amer. Math. Soc. 76 (1954), 234-253. Zbl0055.34002MR62747
  14. [14] A. Kleppner and R.L. Lipsman: The Plancherel formula for group extensions, Ann. Sci. École Norm. Sup. (4) 5 (1972), 459-516. Zbl0239.43003MR342641
  15. [15] R.L. Lipsman: The CCR property for algebraic groups, Amer. J. Math.97 (1975), 741-752. Zbl0319.22009MR390123
  16. [16] G.W. Mackey: Unitary representations of group extensions. I, Acta Math.99 (1958), 265-311. Zbl0082.11301MR98328
  17. [17] D. Montgomery and L. Zippin: Topological transformation groups, Interscience, New York, London, 1955. Zbl0068.01904MR73104
  18. [18] C.C. Moore and J. Rosenberg: Groups with T1-primitive ideal space, J. Functional Analysis22 (1976), 204-224. Zbl0328.22014MR419675
  19. [19] N.V. Pedersen: Semicharacters and solvable Lie groups, Math. Ann.277 (1980), 191-244. Zbl0406.22008MR568989
  20. [20] N.V. Pedersen: On certain KMS-weights on C*-crossed products, Proc. Lond. Math. Soc.44 (1982), 445-472. Zbl0515.46061MR656245
  21. [21] N.V. Pedersen: Semicharacters on connected Lie groups, Duke Math. J.48 (1981), 729-754. Zbl0527.22009MR782574
  22. [22] L. Pukanszky: Leçons sur les représentations des groupes, Dunod, Paris, 1967. Zbl0152.01201MR217220
  23. [23] L. Pukanszky: Characters of algebraic solvable Lie groups, J. Functional Analysis3 (1969), 435-494. Zbl0186.20004MR248287
  24. [24] L. Pukanszky: Actions of algebraic groups of automorphisms on the dual of certain type I groups, Ann. Sci. École Norm. Sup. (4) 5 (1972), 379-395. Zbl0263.22011MR322102
  25. [25] L. Pukanszky: Characters of connected Lie groups, Acta Math. 133 (1974), 81-137. Zbl0323.22011MR409728
  26. [26] L. Pukanszky: Lie groups with completely continuous representations, Bull. Amer. Math. Soc.81 (1975), 1061-1063. Zbl0312.22006MR422516
  27. [27] L. Pukanszky: Unitary representations of Lie groups with cocompact radical and applications, Trans. Amer. Math. Soc.236 (1978), 1-49. Zbl0389.22009MR486313

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.