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

Abstract

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

References in corpus (3)

• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Necklace Lie algebras and noncommutative symplectic geometry
• Equivariant maps between Calogero-Moser spaces

Cited by in corpus (2)

• Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
• On a family of quivers related to the Gibbons-Hermsen system