Keyword: Poisson Lie Algebra : Search

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Deforming $h$ $𝔥$ -trivial the Lie algebra Vect(S¹) inside the Lie algebra of pseudodifferential operators $Ψ 𝒟 𝒪$
- Imed Basdouri,
- Issam Bartouli, and
- Jean Lerbet
International Journal of Geometric Methods in Modern Physics04 May 2017
Preview Abstract
In this paper, we consider the action of Vect(S¹) by Lie derivative on the spaces of pseudodifferential operators $Ψ 𝒟 𝒪$ . We study the $𝔥$ -trivial deformations of the standard embedding of the Lie algebra Vect(S¹) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle $T^{*} S^{1}$ . We classify the deformations of this action that become trivial once restricted to $𝔥$ , where $𝔥 = 𝔞 𝔣 𝔣 (1)$ or $𝔰 𝔩 (2)$ . Necessary and sufficient conditions for integrability of infinitesimal deformations are given.

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