  An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its
exterior algebra. We introduce a graded generalization of the necklace Lie
bialgebra, which depends on a choice of a quiver $Q$. We relate the resulting
Batalin-Vilkovisky structure to the Batalin-Vilkovisky structure coming from a
degree $-1$ symplectic form on a suitably defined representation variety of the
quiver $Q$. The morphism intertwining these Batalin-Vilkovisky algebras will be
given by a twisted trace, recovering the usual (super)trace and the odd trace.
