  In this expository note, we explain the so-called Van den Bergh functor,
which enables the formalization of the Kontsevich-Rosenberg principle, whereby
a structure on an associative algebra has geometric meaning if it induces
standard geometric structures on its representation spaces. Crawley-Boevey,
Etingof and Ginzburg proved that bi-symplectic forms satisfy this principle;
this implies that bi-symplectic algebras can be regarded as noncommutative
symplectic manifolds. In this note, we use the Van den Bergh functor to give an
alternative proof.
