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2014

Maximal Green Sequences of Exceptional Finite Mutation Type Quivers

Seven, Ahmet I.

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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-C\'ordova-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-C\'ordova-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.

Maximal Green Sequences of Exceptional Finite Mutation Type Quivers · Around

Built on

Berenstein A., Fomin S., Zelevinsky A., Cluster algebras. III. Upper bounds and double Bruhat cells,
2005
Earlier work this paper cites.
Fomin S., Zelevinsky A., Cluster algebras. IV. Coefficients,
2007
Earlier work this paper cites.
Derksen H., Owen T., New graphs of finite mutation type,
Original
2008
Earlier work this paper cites.

Similar

Derksen H., Weyman J., Zelevinsky A., Quivers with potentials and their representations II: Applications to cluster algebras,
Original
2010
Cited alongside, same era.
Keller B., On cluster theory and quantum dilogarithm identities, in Representations of Algebras and Related Topics,
Original
2011
Cited alongside, same era.
Nakanishi T., Zelevinsky A., On tropical dualities in cluster algebras, in Algebraic Groups and Quantum Groups,
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2012
Cited alongside, same era.
Canakci I., Lee K., Schiffler R., On cluster algebras from unpunctured surfaces with one marked point,
Original
Cited in the paper.
Cecotti S., Córdova C., Vafa C., Braids, walls and mirrors,
Original
Cited in the paper.

Then

Alim M., Cecotti S., Córdova C., Espahbodi S., Rastogi A., Vafa C., BPS quivers and spectra of complete
Original
2013
Later among the works it cites.
Seven A.I., Maximal green sequences of skew-symmetrizable
Original
2014
Closest in time.
Brüstle T., Dupont G., Pérotin M., On maximal green sequences,
Original
2050
Closest in time.

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