Double quasi-Poisson brackets on associative algebras with involutive anti-automorphisms induce quasi-Poisson structures on twisted representation spaces over arbitrary semisimple bases, with applications to twisted quiver varieties and Hopf algebras with Fox pairings.
A slice theorem for quivers with an involution
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abstract
We study the Luna slice theorem in the case of quivers with an involution or supermixed quivers as introduced by Zubkov. We construct an analogue to the notion of a local quiver setting. We use this technique to determine dimension vectors of simple supermixed representations.
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Quasi-Poisson varieties from double quasi-Poisson algebras in types $B,C,D$
Double quasi-Poisson brackets on associative algebras with involutive anti-automorphisms induce quasi-Poisson structures on twisted representation spaces over arbitrary semisimple bases, with applications to twisted quiver varieties and Hopf algebras with Fox pairings.