Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular categories with transitive Galois actions   In this paper, we study modular categories whose Galois group actions on
their simple objects are transitive. We show that such modular categories admit
unique factorization into prime transitive factors. The representations of
$SL_2(\mathbb{Z})$ associated with transitive modular categories are proven to
be minimal and irreducible. Together with the Verlinde formula, we characterize
prime transitive modular categories as the Galois conjugates of the adjoint
subcategory of the quantum group modular category
$\mathcal{C}(\mathfrak{sl}_2,p-2)$ for some prime $p > 3$. As a consequence, we
completely classify transitive modular categories. Transitivity of
super-modular categories can be similarly defined. A unique factorization of
any transitive super-modular category into s-simple transitive factors is
obtained, and the split transitive super-modular categories are completely
classified.

16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph