Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tits type alternative for groups acting on toric affine varieties   Given a toric affine algebraic variety $X$ and a collection of one-parameter
unipotent subgroups $U_1,\ldots,U_s$ of $\mathop{\rm Aut}(X)$ which are
normalized by the torus acting on $X$, we show that the group $G$ generated by
$U_1,\ldots,U_s$ verifies the following alternative of Tits' type: either $G$
is a unipotent algebraic group, or it contains a non-abelian free subgroup. We
deduce that if $G$ is $2$-transitive on a $G$-orbit in $X$, then $G$ contains a
non-abelian free subgroup, and so, is of exponential growth.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg