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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| Datum: | 2013 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2013
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.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| Zusammenfassung: | 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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