Abstract
We prove the periodicity conjecture for pairs of Dynkin diagrams using Fomin-Zelevinsky’s cluster algebras and their (additive) categorification via triangulated categories.
-
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AUTHOR = {Amiot, Claire},
TITLE = {Cluster categories for algebras of global dimension 2 and quivers with potential},
JOURNAL = {Ann. Inst. Fourier $($Grenoble$)$},
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} -
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author={Inoue, R. and Iyama, O. and Keller, B. and Kuniba, A. and Nakanishi, T.},
TITLE={Periodicities of {$T$} and {$Y$}-systems, dilogarithm identities, and cluster algebras {I}: type {$B_r$}},
NOTE={to appear in \emph{Publ. RIMS}},
ARXIV={1001.1880},
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[InoueIyamaKellerKunibaNakanishi10b] R. Inoue, O. Iyama, B. Keller, A. Kuniba, and T. Nakanishi, Periodicities of $T$ and $Y$-systems, dilogarithm identities, and cluster algebras II: types $C_r$, $F_4$, and $G_2$.
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author={Inoue, R. and Iyama, O. and Keller, B. and Kuniba, A. and Nakanishi, T.},
TITLE={Periodicities of {$T$} and {$Y$}-systems, dilogarithm identities, and cluster algebras {II}: types {$C_r$, $F_4$, and $G_2$}},
ARXIV={1001.1881},
NOTE={to appear in {\it Publ. RIMS}},
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}