  Around 20 years ago, M. Van den Bergh introduced double Poisson brackets as
operations on associative algebras inducing Poisson brackets under the
representation functor. Weaker versions of these operations, called modified
double Poisson brackets, were later introduced by S. Arthamonov in order to
induce a Poisson bracket on moduli spaces of representations of the
corresponding associative algebras. Moreover, he defined two operations that he
conjectured to be modified double Poisson brackets. The first case of this
conjecture was recently proved by M. Goncharov and V. Gubarev motivated by the
theory of Rota-Baxter operators of nonzero weight. We settle the conjecture by
realising the second case as part of a new family of modified double Poisson
brackets.
