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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2013
Автори: Mencattini, I., Tacchella, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2013
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/149193
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149193
record_format dspace
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
spellingShingle A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
Mencattini, I.
Tacchella, A.
title_short 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_sort note on the automorphism group of the bielawski-pidstrygach quiver
author Mencattini, I.
Tacchella, A.
author_facet Mencattini, I.
Tacchella, A.
publishDate 2013
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/149193
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.
work_keys_str_mv AT mencattinii anoteontheautomorphismgroupofthebielawskipidstrygachquiver
AT tacchellaa anoteontheautomorphismgroupofthebielawskipidstrygachquiver
AT mencattinii noteontheautomorphismgroupofthebielawskipidstrygachquiver
AT tacchellaa noteontheautomorphismgroupofthebielawskipidstrygachquiver
first_indexed 2025-12-07T19:52:11Z
last_indexed 2025-12-07T19:52:11Z
_version_ 1850880432953884672