Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The smooth algebra of a one-dimensional singular foliation   Androulidakis and Skandalis showed how to associate a holonomy groupoid, a
smooth convolution algebra and a C*-algebra to any singular foliation. In this
note, we consider the singular foliations of a one-dimensional manifold given
by vector fields that vanish to order k at a point. We show that, whereas the
C*-algebras of these foliations are divided into two isomorphism classes
according to the parity of k, the smooth algebras are pairwise nonisomorphic.
This is accomplished by analyzing certain natural ideals in the smooth
algebras. Issues of factorization with respect to convolution arise and are
resolved using a context-appropriate version of the Diximier-Malliavin theorem.

19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex