Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quivers with relations arising from clusters (A_n case)   Cluster algebras were introduced by S. Fomin and A. Zelevinsky in connection
with dual canonical bases. Let U be a cluster algebra of type A_n. We associate
to each cluster C of U an abelian category Cat_C such that the indecomposable
objects of Cat_C are in natural correspondence with the cluster variables of U
which are not in C. We give an algebraic realization and a geometric
realization of Cat_C. Then, we generalize the ``denominator Theorem'' of Fomin
and Zelevinsky to any cluster.

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The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin