Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformation of Vect($\mathbb{R})$-Modules of Symbols   We consider the action of the Lie algebra of polynomial vector fields,
$\mathfrak{vect}(1)$, by the Lie derivative on the space of symbols
$\mathcal{S}_\delta^n=\bigoplus_{j=0}^n \mathcal{F}_{\delta-j}$. We study
deformations of this action. We exhibit explicit expressions of some 2-cocycles
generating the second cohomology space $\mathrm{H}^2_{\rm
diff}(\mathfrak{vect}(1),{\cal D}_{\nu,\mu})$ where ${\cal D}_{\nu,\mu}$ is the
space of differential operators from $\mathcal{F}_\nu$ to $\mathcal{F}_\mu$.
Necessary second-order integrability conditions of any infinitesimal
deformations of $\mathcal{S}_\delta^n$ are given. We describe completely the
formal deformations for some spaces $\mathcal{S}_\delta^n$ and we give concrete
examples of non trivial deformations.

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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc