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This article is cited in 6 scientific papers (total in 6 papers)
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Ahmet I. Seven Middle East Technical University, Department of Mathematics, 06800, Ankara, Turkey
Abstract:
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti–Córdova–Vafa in the context of supersymmetric gauge theory. The existence of maximal green sequences for exceptional finite mutation type quivers has been shown by Alim–Cecotti–Córdova–Espahbodi–Rastogi–Vafa except for the quiver $X_7$. In this paper we show that the quiver $X_7$ does not have any maximal green sequences. We also generalize the idea of the proof to give sufficient conditions for the non-existence of maximal green sequences for an arbitrary quiver.
Keywords:
skew-symmetrizable matrices; maximal green sequences; mutation classes.
Received: June 18, 2014; in final form August 15, 2014; Published online August 19, 2014
Citation:
Ahmet I. Seven, “Maximal Green Sequences of Exceptional Finite Mutation Type Quivers”, SIGMA, 10 (2014), 089, 5 pp.
Linking options:
https://www.mathnet.ru/eng/sigma954 https://www.mathnet.ru/eng/sigma/v10/p89
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