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A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
Інший ID:
2010 Mathematics Subject Classification: 37K10; 16G20; 14A22
DOI: http://dx.doi.org/10.3842/SIGMA.2013.037
DOI: http://dx.doi.org/10.3842/SIGMA.2013.037
Посилання:
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.
Підтримка:
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.).
Дата:
2013
Переглядів:
707
Завантажень:
254
Анотація:
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.
