Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hall algebras and the Quantum Frobenius   Lusztig has constructed a Frobenius morphism for quantum groups at an
$\ell$-th root of unity, which gives an integral lift of the Frobenius map on
universal enveloping algebras in positive characteristic. Using the Hall
algebra we give a simple construction of this map for the positive part of the
quantum group attached to an arbitrary Cartan datum in the nondivisible case.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs