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Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
Інший ID:
2010 Mathematics Subject Classification: 15B36; 05C50
DOI:10.3842/SIGMA.2014.089
DOI:10.3842/SIGMA.2014.089
Посилання:
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers / A.I. Seven // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 11 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
The author’s research was supported in part by the Scientific and Technological Research Council.
of Turkey (TUBITAK) grant # 113F138. The author also thanks Christof f Geiss for drawing
his attention to the paper [1] by presenting its results at the Workshop on Hall and Cluster
Algebras in CRM, University of Montreal. He also thanks the organizers for organizing the
conference.
Дата:
2014
Переглядів:
439
Завантажень:
256
Анотація:
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 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.
