Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Gel'fand-Kolmogoroff type results   We prove that a vector bundle $ E \to M$ is characterized by the associative
structure of the space of symbols of the Lie algebra generated by all
differential operators on $E$ which are eigenvectors of the Lie derivative in
the direction of the Euler vector field.
  We also obtain similar result with the $\mathbb{R}-$ algebra of smooth
functions which are polynomial along the fibers of $E.$ This allows us to
deduce a Gel'fand-Kolmogoroff type result for the $\mathbb{R}-$algebra ${\rm
Pol}(T^*(M))$ of symbols of the differential operators of $M.$

19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph