A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
We show that there exists a morphism between a group Γalg introduced by G. Wilson and a quotient of the group of tame symplectic automorphisms of the path algebra of a quiver introduced by Bielawski and Pidstrygach. The latter is known to act transitively on the phase space Cn,₂ of the Gibbons-Herms...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2013 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149193 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver / I. Mencattini, A. Tacchella // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736117814525952 |
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| author | Mencattini, I. Tacchella, A. |
| author_facet | Mencattini, I. Tacchella, A. |
| citation_txt | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver / I. Mencattini, A. Tacchella // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show that there exists a morphism between a group Γalg introduced by G. Wilson and a quotient of the group of tame symplectic automorphisms of the path algebra of a quiver introduced by Bielawski and Pidstrygach. The latter is known to act transitively on the phase space Cn,₂ of the Gibbons-Hermsen integrable system of rank 2, and we prove that the subgroup generated by the image of Γalg together with a particular tame symplectic automorphism has the property that, for every pair of points of the regular and semisimple locus of Cn,₂, the subgroup contains an element sending the first point to the second.
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| first_indexed | 2025-12-07T19:52:11Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149193 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:52:11Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
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| spelling | Mencattini, I. Tacchella, A. 2019-02-19T18:28:22Z 2019-02-19T18:28:22Z 2013 A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver / I. Mencattini, A. Tacchella // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 16 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K10; 16G20; 14A22 DOI: http://dx.doi.org/10.3842/SIGMA.2013.037 https://nasplib.isofts.kiev.ua/handle/123456789/149193 We show that there exists a morphism between a group Γalg introduced by G. Wilson and a quotient of the group of tame symplectic automorphisms of the path algebra of a quiver introduced by Bielawski and Pidstrygach. The latter is known to act transitively on the phase space Cn,₂ of the Gibbons-Hermsen integrable system of rank 2, and we prove that the subgroup generated by the image of Γalg together with a particular tame symplectic automorphism has the property that, for every pair of points of the regular and semisimple locus of Cn,₂, the subgroup contains an element sending the first point to the second. The authors would like to thank Claudio Bartocci, Yuri Berest, Roger Bielawski, Ugo Bruzzo,
 Benoit Dherin, Letterio Gatto, Victor Ginzburg, Hiraku Nakajima, George Wilson and the
 anonymous referees for some useful comments about a previous version of this manuscript. Both
 authors are grateful to FAPESP for supporting the present work with the grants 2010/19201-8
 (I.M.) and 2011/09782-6 (A.T.). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver Article published earlier |
| spellingShingle | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver Mencattini, I. Tacchella, A. |
| title | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver |
| title_full | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver |
| title_fullStr | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver |
| title_full_unstemmed | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver |
| title_short | A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver |
| title_sort | note on the automorphism group of the bielawski-pidstrygach quiver |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149193 |
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