# On Martin Bordemann's proof of the existence of projectively equivariant quantizations

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 793-800
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topPierre Lecomte. "On Martin Bordemann's proof of the existence of projectively equivariant quantizations." Open Mathematics 2.5 (2004): 793-800. <http://eudml.org/doc/268681>.

@article{PierreLecomte2004,

abstract = {The paper explains the notion of projectively equivariant quantization. It gives a sketch of Martin Bordemann's proof of the existence of projectively equivariant quantization on arbitrary manifolds.},

author = {Pierre Lecomte},

journal = {Open Mathematics},

keywords = {53C05; 53D55},

language = {eng},

number = {5},

pages = {793-800},

title = {On Martin Bordemann's proof of the existence of projectively equivariant quantizations},

url = {http://eudml.org/doc/268681},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Pierre Lecomte

TI - On Martin Bordemann's proof of the existence of projectively equivariant quantizations

JO - Open Mathematics

PY - 2004

VL - 2

IS - 5

SP - 793

EP - 800

AB - The paper explains the notion of projectively equivariant quantization. It gives a sketch of Martin Bordemann's proof of the existence of projectively equivariant quantization on arbitrary manifolds.

LA - eng

KW - 53C05; 53D55

UR - http://eudml.org/doc/268681

ER -

## References

top- [1] F. Boniver, H. Hansoul, P. Mathonet and N. Poncin: “Equivariant symbol calculus for differential operators acting on forms”, Lett. Math. Phys., Vol. 62(3), (2002), pp. 219–232. http://dx.doi.org/10.1023/A:1022251607566 Zbl1035.17034
- [2] M. Bordemann: “Sur l'existence d'une prescription d'ordre naturelle projectivement invariante” (arXiv:math.DG/0208171v1 22Aug2002).
- [3] S. Bouarroudj: “Projectively equivariant quantization map”, Lett. Math. Phys., Vol. 51(4), (2000), pp. 265–274. http://dx.doi.org/10.1023/A:1007692910159 Zbl1067.53071
- [4] S. Bouarroudj: “Formula for the projectively invariant quantization on degree three”, C. R. Acad. Sci. Paris Sér. I Math., Vol. 333(4), (2001), pp. 34–346. Zbl0997.53015
- [5] C. Duval, P. Lecomte and V. Ovsienko: “Conformally equivariant quantization: existence and uniqueness”, Ann. Inst. Fourier (Grenoble), Vol. 49(6), (1999), pp. 1999–2029. Zbl0932.53048
- [6] S. Kobayashi: Transformation groups in differential geometry, Springer, Berlin, 1972. Zbl0246.53031
- [7] P. Lecomte: “Towards projectively equivariant Quantization. Noncommutative geometry and string theory”, Meada at al. (Eds.): Progress in theoretical physics, Vol. 144, (2001), pp. 125–132. Zbl1012.53069
- [8] P. Lecomte: “On the cohomology of sl(m+1,ℝ) acting on differential Operators and sl(m+1,ℝ) symbols”, Indaga. Math., NS, Vol. 11(1), (2000), pp. 95–114. http://dx.doi.org/10.1016/S0019-3577(00)88577-8
- [9] P. Lecomte and V. Ovsienko: “Projectively equivariant Symbol Calculus”, Letters in Math. Phys., Vol. 49, (1999), pp. 173–196. http://dx.doi.org/10.1023/A:1007662702470 Zbl0989.17015
- [10] P. Lecomte and V. Ovsienko: “Cohomology of the Vector Fields Lie Algebra and Modules of differential Operators on a smooth Manifold”, Comp. Math., Vol. 124, (2000), pp. 95–110. http://dx.doi.org/10.1023/A:1002447724679 Zbl0968.17007
- [11] P. Mathonet and F. Boniver: “Maximal subalgebras of vector fields for equivariant quantizations”, J. Math. Phys., Vol. 42(2), (2001), pp. 582–589. http://dx.doi.org/10.1063/1.1332782 Zbl1032.17041

## NotesEmbed ?

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