Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Atomic basis of quantum cluster algebra of type $\widetilde{A}_{2n-1,1}$   Let $Q$ be the affine quiver of type $\widetilde{A}_{2n-1,1}$ and
$\mathcal{A}_{q}(Q)$ be the quantum cluster algebra associated to the valued
quiver $(Q,(2,2,\dots,2))$. We prove some cluster multiplication formulas, and
deduce that the cluster variables associated with vertices of $Q$ satisfy a
quantum analogue of the constant coefficient linear relations. We then
construct two bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases
$\mathcal{B}$ and $\mathcal{S}$ of $\mathcal{A}_{q}(Q)$ consisting of positive
elements, and prove that $\mathcal{B}$ is an atomic basis.

10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
14
The categories of this paper are: math-ph