Friezes, Strings and Cluster Variables

Mathematics – Commutative Algebra

Scientific paper

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Some minor typos were fixed and some sections were shortened; to appear in Glasgow Mathematical Journal (2011) 32 pages

Scientific paper

To any walk in a quiver, we associate a Laurent polynomial. When the walk is
the string of a string module over a 2-Calabi-Yau tilted algebra, we prove that
this Laurent polynomial coincides with the corresponding cluster character of
the string module, up to an explicit normalising monomial factor.

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