  We study the Drinfeld double of the (equivariant spherical) Cohomological
Hall algebra in the sense of Kontsevich and Soibelman, associated to a smooth
toric Calabi-Yau 3-fold $X$. By general reasons, the COHA acts on the
cohomology of the moduli spaces of certain perverse coherent systems on $X$ via
"raising operators". Conjecturally the COHA action extends to an action of the
Drinfeld double by adding the "lowering operators".
  In this paper, we show that the Drinfeld double is a generalization of the
notion of the Cartan doubled Yangian defined earlier by Finkelberg and others.
We extend this "$3d$ Calabi-Yau perspective" on the Lie theory furthermore by
associating a root system to certain families of $X$. We formulate a conjecture
that the above-mentioned action of the Drinfeld double factors through a
shifted Yangian of the root system. The shift is explicitly determined by the
moduli problem and the choice of stability conditions, and is expressed
explicitly in terms of an intersection number in $X$. We check the conjectures
in several examples, including a special case of an earlier conjecture of
Costello.
