Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The deformation quantizations of the hyperbolic plane   We describe the space of (all) invariant deformation quantizations on the
hyperbolic plane as solutions of the evolution of a second order hyperbolic
differential operator. The construction is entirely explicit and relies on
non-commutative harmonic analytical techniques on symplectic symmetric spaces.
The present work presents a unified method producing every quantization of the
hyperbolic plane, and provides, in the 2-dimensional context, an exact solution
to Weinstein's WKB quantization program within geometric terms. The
construction reveals the existence of a metric of Lorentz signature canonically
attached (or `dual') to the geometry of the hyperbolic plane through the
quantization process.

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The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys