Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
By Ahmet I. Seven. 2014
17 citations recorded by the source corpus.
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and in- dependently 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 X7. In this paper we show that the quiver X7 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.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
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In Algebra and Number Theory
- Laurent Demonet
- B. Keller
- Pierre-Guy Plamondon
- I. Reiten
- Bernard Leclerc
- Osamu Iyama
- Alexander Kuznetsov
- Ralf Schiffler
In Discrete Mathematics and Combinatorics
- Laurent Demonet
- B. Keller
- S. Cecotti
- C. Vafa
- Greg Muller
- David E. Speyer
- Alexander Garver
- Thomas McConville
In Geometry and Topology
- Laurent Demonet
- B. Keller
- Pierre-Guy Plamondon
- I. Reiten
- Osamu Iyama
- Bernard Leclerc
- Alexander Kuznetsov
- Ralf Schiffler
Citations in the corpus
- A survey on maximal green sequences (2019, background): “Seven shows in [106] that the quivers in the mutation class of the quiver X7 (discovered in [34]) do not admit maximal green sequences (and presumably no reddening sequences either).”