Maximal Green Sequences of Exceptional Finite Mutation Type Quivers
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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146610 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862750432695156736 |
|---|---|
| author | Seven, A.I. |
| author_facet | Seven, A.I. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T21:05:23Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146610 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:05:23Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Seven, A.I. 2019-02-10T10:00:29Z 2019-02-10T10:00:29Z 2014 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. 1815-0659 2010 Mathematics Subject Classification: 15B36; 05C50 DOI:10.3842/SIGMA.2014.089 https://nasplib.isofts.kiev.ua/handle/123456789/146610 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Maximal Green Sequences of Exceptional Finite Mutation Type Quivers Article published earlier |
| spellingShingle | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers Seven, A.I. |
| title | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_full | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_fullStr | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_full_unstemmed | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_short | Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_sort | maximal green sequences of exceptional finite mutation type quivers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146610 |
| work_keys_str_mv | AT sevenai maximalgreensequencesofexceptionalfinitemutationtypequivers |