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

• Autorzy: Pierre Lecomte
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Quantization; projective structure; differential operators; smooth manifolds; 53C05; 53D55

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 5
• Strony: 793-800

Daty

wydano

2004-10-01

online

2004-10-01

Twórcy

autor

Pierre Lecomte

• University of Liege

Bibliografia

• [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
• [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
• [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.
• [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.
• [6] S. Kobayashi: Transformation groups in differential geometry, Springer, Berlin, 1972.
• [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.
• [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
• [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
• [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

Identyfikatory

DOI

10.2478/BF02475977