A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver.

Ginzburg, Bocklandt, and Le Bruyn defined an infinite-dimensional Lie algebra canonically associated to any quiver. Following suggestions of V. Turaev, P. Etingof, and Ginzburg, we define a cobracket and prove that it defines a Lie bialgebra structure. We then present a Hopf algebra quantizing this Lie bialgebra and prove that it is a Hopf algebra satisfying the Poincaré-Birkhoff-Witt (PBW) property. We also define representations to differential operators quantizing the trace representations of the Lie algebra defined by Ginzburg. [ABSTRACT FROM AUTHOR]