A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver

Symmetry Integrability and Geometry-Methods and Applications

article

Igor Mencattini¹  Alberto Tacchella¹ 

[1] ICMC - Universidade de São Paulo

关键词: Gibbons–Hermsen system;    quiver varieties;    noncommutative symplectic geometry;    integrable systems;   

DOI  :  10.3842/SIGMA.2013.037

来源: National Academy of Science of Ukraine

【 摘 要 】

We show that there exists a morphism between a group Γ alg 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 C n ,2 of the Gibbons-Hermsen integrable system of rank 2, and we prove that the subgroup generated by the image of Γ alg together with a particular tame symplectic automorphism has the property that, for every pair of points of the regular and semisimple locus of C n ,2 , the subgroup contains an element sending the first point to the second.

【 授权许可】

Unknown