Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 4 (2008), 065, 19 pages      math.RT/0702712      http://dx.doi.org/10.3842/SIGMA.2008.065
Contribution to the Special Issue on Deformation Quantization

sl(2)-Trivial Deformations of VectPol(R)-Modules of Symbols

Mabrouk Ben Ammar and Maha Boujelbene
Département de Mathématiques, Faculté des Sciences de Sfax, BP 802, 3038 Sfax, Tunisie

Received January 14, 2008, in final form September 05, 2008; Published online September 18, 2008
Mistake in Proposition 4 and further computations have been corrected November 18, 2008.

Abstract
We consider the action of VectPol(R) by Lie derivative on the spaces of symbols of differential operators. We study the deformations of this action that become trivial once restricted to sl(2). Necessary and sufficient conditions for integrability of infinitesimal deformations are given.

Key words: tensor densities, cohomology, deformations.

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