Semi-groupe de Lie associé à un cône symétrique

Khalid Koufany

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 1, page 1-29
  • ISSN: 0373-0956

Abstract

top
To any formally real Jordan algebra one may attach a symmetric cone. We study the sub-semigroup of elements of the conformal group which map the cone into itself.

How to cite

top

Koufany, Khalid. "Semi-groupe de Lie associé à un cône symétrique." Annales de l'institut Fourier 45.1 (1995): 1-29. <http://eudml.org/doc/75114>.

@article{Koufany1995,
abstract = {Soit $V$ une algèbre de Jordan simple euclidienne de dimension finie et $\Omega $ le cône symétrique associé. Nous étudions dans cet article le semi-groupe $\Gamma $, naturellement associé à $V$, formé des automorphismes holomorphes du domaine tube $T_\{\Omega \}:=V+i\Omega $ qui appliquent le cône $\Omega $ dans lui-même.},
author = {Koufany, Khalid},
journal = {Annales de l'institut Fourier},
keywords = {Hermitian symmetric domain; Jordan algebra; conformal group; symmetric space of Cayley type; Ol'shanskij semigroup},
language = {fre},
number = {1},
pages = {1-29},
publisher = {Association des Annales de l'Institut Fourier},
title = {Semi-groupe de Lie associé à un cône symétrique},
url = {http://eudml.org/doc/75114},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Koufany, Khalid
TI - Semi-groupe de Lie associé à un cône symétrique
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 1
SP - 1
EP - 29
AB - Soit $V$ une algèbre de Jordan simple euclidienne de dimension finie et $\Omega $ le cône symétrique associé. Nous étudions dans cet article le semi-groupe $\Gamma $, naturellement associé à $V$, formé des automorphismes holomorphes du domaine tube $T_{\Omega }:=V+i\Omega $ qui appliquent le cône $\Omega $ dans lui-même.
LA - fre
KW - Hermitian symmetric domain; Jordan algebra; conformal group; symmetric space of Cayley type; Ol'shanskij semigroup
UR - http://eudml.org/doc/75114
ER -

References

top
  1. [1] Ph. BOUGEROL, Kalman filtring with random coefficients and contractions, SIAM. J. Control and Optimization, 31 (1993), 942-959. Zbl0785.93040
  2. [2] H. BRAUN & M. KOECHER, Jordan Algebren, Springer, 1975. Zbl0145.26001
  3. [3] N. DÖRR, On Ol'shanskiĩ semigroup, Math. Ann., 288 (1990), 21-33. Zbl0694.22013
  4. [4] J. FARAUT, Algèbres de Jordan et cônes symétriques, Écoles d'été du CIMPA, Université de Poitiers, 1989. 
  5. [5] J. FARAUT, Espaces symétriques ordonnés et algèbres de Volterra, J. of Math. Soc. Japan, 43, 1 (1991), 133-146. Zbl0732.43005MR92d:22019
  6. [6] J. FARAUT, Fonctions sphériques sur un espace symétrique ordonné de type Cayley, Preprint, avril 1994. 
  7. [7] J. FARAUT & A. KORANYI, Analysis on symmetric cones, À paraître, Oxford University Press. Zbl0841.43002
  8. [8] J. FARAUT, J. HILGERT & G. ÓLAFSSON, Spherical functions on ordered symmetric spaces, Preprint, July 1993. Zbl0810.43003
  9. [9] S. HELGASON, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press. New York-London, 1978. Zbl0451.53038
  10. [10] J. HILGERT, K.H. HOFMANN & J.D. LAWSON, Lie groups, convex cones, and semigroups Oxford University Press, 1989. Zbl0701.22001MR91k:22020
  11. [11] J. HILGERT, G. ÓLAFSSON & B. ØERSTED, Hardy spaces on affine symmetric spaces, J. reine angew. Math., 415 (1991), 189-218. Zbl0716.43006MR92h:22030
  12. [12] M. KOECHER, Die Geodätischen von Positivitätsbereichen, Math. Ann., 135 (1958), 192-202. Zbl0083.07202MR21 #2749
  13. [13] M. KOECHER, Jordan algebras and their applications, Lectures notes, Univ. of Minnesota, Minneapolis, 1962. Zbl0128.03101
  14. [14] M. KOECHER, An elementary approach to bounded symmetric domains, Lectures notes, Rice University, 1969. Zbl0217.10901MR41 #5652
  15. [15] A. KORANYI, Complex analysis and symmetric domains, École d'été du CIMPA, Université de Poitiers, 1988. 
  16. [16] K. KOUFANY, Semi-groupe de Lie associé à une algèbre de Jordan euclidienne, Doctorat de l'Université de Nancy I, octobre 1993. 
  17. [17] K. KOUFANY, Réalisation des espaces symétriques de type Cayley, C.R. Acad. Sci. Paris, 318, Série I (1994), 425-428. Zbl0839.53035MR95h:32036
  18. [18] J.D. LAWSON, Polar and Ol'shanskiĩ decompositions, Seminaire Sophus Lie, 1, 2 (1991), 163-173. Zbl0760.22006MR93d:22025
  19. [19] O. LOOS, Jordan pairs, Lectures Notes in Math. 460, Springer, 1974. 
  20. [20] O. LOOS, Bounded symmetric domains and Jordan pairs, Lectures notes, University of California, Irvine, 1977. Zbl0228.32012
  21. [21] K.-H. NEEB, Holomorphic representation theory I, Preprint, 1993. 
  22. [22] K.-H. NEEB, Holomorphic representation theory II, Preprint, 1993. 
  23. [23] K.-H. NEEB, Holomorphic representation theory III, Preprint, 1993. 
  24. [24] G. ÓLAFSSON, Causal symmetric spaces, Math. Gotting., 15 1990. 
  25. [25] G.I. OL'SHANSKIĨ, Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series, Funct. Anal. Appl., 15 (1982), 275-285. Zbl0503.22011
  26. [26] G.I. OL'SHANSKIĨ, Convex cones in symmetric Lie algebras, Lie semigroups and invariant causal (order) structures on pseudo-Riemannian symmetric spaces, Soviet Math. Dokl., 26 (1982), 97-101. Zbl0512.22012
  27. [27] G.I. OL'SHANSKIĨ, Complex Lie semigroups, Hardy spaces and the Gelfand Gindikin program, Topics in group theory and homological algebra, Varoslavl University Press, 1982, p. 85-98 (Russian); English translation in Differential Geometry and its Applications, 1 (1991), 235-246. 
  28. [28] I. SATAKE, Algebraic structures of symmetric domains, Iwanami-Shoten and Princeton Univ. Press, 1980. Zbl0483.32017MR82i:32003
  29. [29] E.B. VINBERG, Homogeneous cones, Soviet Math. Dokl., 1 (1960), 787-790. Zbl0143.05203MR25 #5077
  30. [30] M. WOJTKOWSKI, Invariant families of cones and Lyapunov exponents, Ergod. Theo. and Dyn. Sys., 5 (1985), 145-161. Zbl0578.58033MR86h:58090

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.