On infinite Lie groups

Alexandre A. Martins Rodrigues

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 3, page 245-274
  • ISSN: 0373-0956

Abstract

top
Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie pseudo-groups is introduced and the notions of morphism kernel and quotient are defined for the equivalence classes. In the special case of transitive pseudo-groups or of pseudo-groups of finite type the regularity conditions are always satisfied.

How to cite

top

Rodrigues, Alexandre A. Martins. "On infinite Lie groups." Annales de l'institut Fourier 31.3 (1981): 245-274. <http://eudml.org/doc/74506>.

@article{Rodrigues1981,
abstract = {Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie pseudo-groups is introduced and the notions of morphism kernel and quotient are defined for the equivalence classes. In the special case of transitive pseudo-groups or of pseudo-groups of finite type the regularity conditions are always satisfied.},
author = {Rodrigues, Alexandre A. Martins},
journal = {Annales de l'institut Fourier},
keywords = {analytic Lie pseudo-groups},
language = {eng},
number = {3},
pages = {245-274},
publisher = {Association des Annales de l'Institut Fourier},
title = {On infinite Lie groups},
url = {http://eudml.org/doc/74506},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Rodrigues, Alexandre A. Martins
TI - On infinite Lie groups
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 3
SP - 245
EP - 274
AB - Under some regularity conditions one proves that quotients and kernels of infinitesimal analytic Lie pseudo-groups by invariant fiberings are again infinitesimal Lie pseudo-groups. The regularity conditions are shown to be necessary and sufficient if one wishes both quotient and kernel to be infinitesimal Lie pseudo-groups. One defines and proves the existence of the quotient of an infinitesimal Lie pseudo-group by a normal sub-pseudo group. An equivalence relation for germs of infinitesimal Lie pseudo-groups is introduced and the notions of morphism kernel and quotient are defined for the equivalence classes. In the special case of transitive pseudo-groups or of pseudo-groups of finite type the regularity conditions are always satisfied.
LA - eng
KW - analytic Lie pseudo-groups
UR - http://eudml.org/doc/74506
ER -

References

top
  1. [1] E. CARTAN, La structure des groupes infinis, Ţuvres complètes : II, vol. 2, Gauthier-Villars, Paris, 1953, pp. 1335-1384. 
  2. [2] H. GOLDSCHMIDT, Existence theorems for analytic linear partial differential equations, Ann. of Math., 86, (1967), 246-270. Zbl0154.35103MR36 #2933
  3. [3] H. GOLDSCHMIDT, Prolongations of linear partial differential equations : I-A conjecture of E. Cartan, Ann. Sci. Ec. Norm. Sup., (4) 1 (1968), 417-444. Zbl0167.09402MR38 #3888
  4. [4] M. KURANISHI, A.A.M. RODRIGUES, Quotients of pseudo-groups by invariant fiberings, Nagoya Math., J., 24 (1964), 109-128. Zbl0163.45301MR29 #5962
  5. [5] M. KURANISHI, On the local theory of continuous infinite pseudo-groups. I, II, Nagoya Math. J., 15 (1959), 225-260 ; 19 (1961), 55-91. Zbl0212.56501
  6. [6] M. KURANISHI, Lectures on involutive systems of partial differential equations, Publicações da Sociedade de Matemática de São Paulo, São Paulo, (1967). Zbl0163.12001
  7. [7] A. PETITJEAN, A.A.M. RODRIGUES, Correspondance entre algèbres de Lie abstraites et pseudo-groupes de Lie transitifs, Annals of Math., vol. 101 (1975), 268-279. Zbl0333.22010MR52 #6800
  8. [8] Ngô Van QUÊ, Du prolongement des espaces fibrés et des structures infinitésimales, Ann. Inst. Fourier, (Grenoble), 17 (1967), 157-223. Zbl0157.28506MR36 #4468
  9. [9] QUILLEN, Formal properties of over-determined system of linear partial differential equations (Ph. D. thesis, Harvard, 1964). 
  10. [10] A.A.M. RODRIGUES, G-structures et pseudo groupes de Lie, Notes d'un cours donné à l'Université de Grenoble (1968). 
  11. [11] A.A.M. RODRIGUES, Sur le noyau d'un pseudo-groupe de Lie infinitésimal involutif transitif par rapport à une fibration invariante, C.R. Acad. Sci., Paris, Sér. A, 269 (1969), 1154-1155. Zbl0194.52704MR41 #2722
  12. [12] A.A.M. RODRIGUES, Sur le quotient d'un pseudo-groupe de Lie infinitésimal transitif par une fibration invariante, C.R. Acad. Sci., Paris, Sér. A, 269 (1969), 1211-1213. Zbl0194.52801MR41 #2723
  13. [13] I.M. SINGER, S. STERNBERG, The infinite groups of Lie and Cartan, I, J. D'Analyse Math., 15 (1965). Zbl0277.58008MR36 #911

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.