%0 Journal Article
%T A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver
%A Igor Mencattini
%A Alberto Tacchella
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2013
%I National Academy of Science of Ukraine
%R 10.3842/sigma.2013.037
%X We show that there exists a morphism between a group ¦£^{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 ¦£^{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.
%K Gibbons-Hermsen system
%K quiver varieties
%K noncommutative symplectic geometry
%K integrable systems
%U http://dx.doi.org/10.3842/SIGMA.2013.037