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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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Інститут математики НАН України
2014
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146610 |
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irk-123456789-1466102019-02-11T01:23:18Z Maximal Green Sequences of Exceptional Finite Mutation Type Quivers Seven, A.I. 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. 2014 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146610 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| 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. |
| format |
Article |
| author |
Seven, A.I. |
| spellingShingle |
Seven, A.I. Maximal Green Sequences of Exceptional Finite Mutation Type Quivers Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Seven, A.I. |
| author_sort |
Seven, A.I. |
| title |
Maximal Green Sequences of Exceptional Finite Mutation Type Quivers |
| title_short |
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_sort |
maximal green sequences of exceptional finite mutation type quivers |
| publisher |
Інститут математики НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146610 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sevenai maximalgreensequencesofexceptionalfinitemutationtypequivers |
| first_indexed |
2023-05-20T17:25:12Z |
| last_indexed |
2023-05-20T17:25:12Z |
| _version_ |
1796153253944098816 |