Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic Operators Associated with Groups of Quantized Canonical
  Transformations   Given a Lie group $G$ of quantized canonical transformations acting on the
space $L^2(M)$ over a closed manifold $M$, we define an algebra of so-called
$G$-operators on $L^2(M)$. We show that to $G$-operators we can associate
symbols in appropriate crossed products with $G$, introduce a notion of
ellipticity and prove the Fredholm property for elliptic elements. This
framework encompasses many known elliptic theories, for instance, shift
operators associated with group actions on $M$, transversal elliptic theory,
transversally elliptic pseudodifferential operators on foliations, and Fourier
integral operators associated with coisotropic submanifolds.

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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat