Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Dixmier-Malliavin theorem for Lie groupoids   A famous theorem of Dixmier-Malliavin asserts that every smooth,
compactly-supported function on a Lie group can be expressed as a finite sum in
which each term is the convolution, with respect to Haar measure, of two such
functions. We establish that the same holds for a Lie groupoid. Most of the
heavy lifting is done by a lemma in the original work of Dixmier-Malliavin. We
also need the technology of Lie algebroids and the corresponding notion of
exponential map. As an application, we obtain a result on the arithmetic of
ideals in the smooth convolution algebra of a Lie groupoid arising from
functions vanishing to given order on an invariant submanifold of the unit
space.

0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg