Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the quantization of $C^{\infty}(\mathbb R^d)$   An infinitesimal deformation of $C^{\infty}(\mathbb R^d)$ has a vanishing
primary obstruction if and only if its skew form is Poisson, and therefore is
integrable to a full deformation of $C^{\infty}(\mathbb R^d)$ by the work of
Kontsevich. This is further equivalent to having its coefficients satisfy a set
of $\binom{d}{3}$ nonlinear partial differential equations. The single such
equation in the case $d=3$ suggests that a big bang might be localized to an
instant in time and point in space. This note also reexamines the Basic
Universal Deformation Formula (UDF) which asserts that if $D_1, D_2$ are
commuting derivations of an associative algebra $\mathcal{A}$ over the
rationals then exponentiation of $D_1\smile D_2$ provides a full deformation of
$\mathcal{A}$. It gives further applications to quantization and to UDFs with
non-commuting derivations.

28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin