Space of Second Order Linear Differential Operators As a Module Over the Lie Algebra of Vector Fields

C. Duval; V. Yu. Ovsienko

Recherche Coopérative sur Programme n°25 (1995)

  • Volume: 47, page 193-213

How to cite

top

Duval, C., and Ovsienko, V. Yu.. "Space of Second Order Linear Differential Operators As a Module Over the Lie Algebra of Vector Fields." Recherche Coopérative sur Programme n°25 47 (1995): 193-213. <http://eudml.org/doc/274923>.

@article{Duval1995,
author = {Duval, C., Ovsienko, V. Yu.},
journal = {Recherche Coopérative sur Programme n°25},
language = {eng},
pages = {193-213},
publisher = {Institut de Recherche Mathématique Avancée - Université Louis Pasteur},
title = {Space of Second Order Linear Differential Operators As a Module Over the Lie Algebra of Vector Fields},
url = {http://eudml.org/doc/274923},
volume = {47},
year = {1995},
}

TY - JOUR
AU - Duval, C.
AU - Ovsienko, V. Yu.
TI - Space of Second Order Linear Differential Operators As a Module Over the Lie Algebra of Vector Fields
JO - Recherche Coopérative sur Programme n°25
PY - 1995
PB - Institut de Recherche Mathématique Avancée - Université Louis Pasteur
VL - 47
SP - 193
EP - 213
LA - eng
UR - http://eudml.org/doc/274923
ER -

References

top
  1. [1] R. J. Blattner, Quantization and representation theory, in "Proc. Sympos. Pure Math.," Vol. 26, AMS, Providence, 145-165, 1974. Zbl0296.53031MR341529
  2. [2] E. Cartan, "Leçons sur la théorie des espaces à connexion projective." Gauthier-Villars, Paris, 1937. Zbl0016.07603JFM63.0689.05
  3. [3] C. Duval, J. Elhadad And G. M. Tuynman,The BRS Method and Geometric Quantization: Some Examples, Comm. Math. Phys.126 (1990), 535-557. Zbl0699.58040MR1032872
  4. [4] B. L. Feigin, D. B. Fuks, Homology of the Lie algebra of vector fields on the line, Func. Anal Appl.14 (1980), 201-212. Zbl0487.57011MR583800
  5. [5] D. B. Fuks, "Cohomology of infinite-dimensional Lie algebras," Consultants Bureau, New York, 1987. Zbl0667.17005MR874337
  6. [6] A. A. Kirillov, Infinite dimensional Lie groups: their orbits, invariants and representations. The geometry of moments, in "Lecture Notes in Math." Vol. 970, Springer-Verlag, 1982. Zbl0498.22017MR699803
  7. [7] A. A. Kirlllov, Geometric Quantization, in "Encyclopedia of Math. Sci.," Vol. 4, Springer-Verlag, 1990. Zbl0780.58024
  8. [8] A. A. Kirlllov, Invariant Differential Operators over Geometric Quantities, in "Modern Problems in Mathematics," VINITI (in Russian), Vol. 16, 1980. 
  9. [9] B. Kostant, Quantization and Unitary Representations, in "Lecture Notes in Math.," Springer-Verlag, Vol. 170, 1970. Zbl0223.53028MR294568
  10. [10] B. Kostant, Symplectic Spinors, in "Symposia Math.," Vol. 14, London, Acad. Press, 1974. Zbl0321.58015MR400304
  11. [11] P.B.A. Lecomte, P. Mathonet, E. Tusset, Comparison of some modules of the Lie algebra of vector fields, Preprint Univ. of Liège, 1995. 212 Zbl0892.58002
  12. [12] O. D. Ovsienko, V. Yu. Ovsienko, Lie derivative of order n on a line. Tensor meaning of the Gelfand-Dickey bracket, in "Adv. in Soviet Math." Vol. 2, 1991. Zbl0753.58008MR1104942
  13. [13] J. Rawnsley, A nonunitary pairing of polarizations for the Kepler problem, Trans. AMS250 (1979), 167-180. Zbl0422.58019MR530048
  14. [14] A. N. Rudakov, Irreducible representations of infinite-dimensional Lie algebras of Cartan type, Math. USSR Izvestija8 (1974), 836-866. Zbl0322.17004MR360732
  15. [15] J. Sniatycki, "Geometric quantization and quantum mechanics," Springer-Verlag, Berlin, 1980. Zbl0429.58007MR554085
  16. [16] J.-M. Souriau, "Structure des systèmes dynamiques," Paris, Dunod, © 1969 Zbl0186.58001
  17. [16] J.-M. Souriau, "Structure des systèmes dynamiques," Paris, Dunod, ©1970. Zbl0186.58001MR260238
  18. [17] N. M. J. Woodhouse, "Geometric Quantization," Clarendon Press, Oxford, 1992. Zbl0747.58004MR1183739

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.