Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classification of Zamolodchikov periodic quivers   Zamolodchikov periodicity is a property of certain discrete dynamical systems
associated with quivers. It has been shown by Keller to hold for quivers
obtained as products of two Dynkin diagrams. We prove that the quivers
exhibiting Zamolodchikov periodicity are in bijection with pairs of commuting
Cartan matrices of finite type. Such pairs were classified by Stembridge in his
study of $W$-graphs. The classification includes products of Dynkin diagrams
along with four other infinite families, and eight exceptional cases. We
provide a proof of Zamolodchikov periodicity for all four remaining infinite
families, and verify the exceptional cases using a computer program.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org