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arXiv · 1208.3613

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

Igor Mencattini·Alberto Tacchella
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Abstract

We show that there exists a morphism between a group $Γ^{\mathrm{alg}}$ 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 $Γ^{\mathrm{alg}}$ 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.

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Igor Mencattini, Alberto Tacchella. 2013-04-30. A Note on the Automorphism Group of the Bielawski-Pidstrygach Quiver. https://doi.org/10.3842/sigma.2013.037

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