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We introduce a new perverse filtration on the Borel-Moore homology of thestack of representations of a preprojective algebra $\Pi_Q$, for arbitrary $Q$,by proving that the derived direct image of the dualizing mixed Hodge modulealong the morphism to the coarse moduli space is pure. We show that the zerothpiece of the resulting filtration on the preprojective CoHA is isomorphic tothe universal enveloping algebra of an associated BPS Lie algebra$\mathfrak{g}_{\Pi_Q}$, and that the spherical Lie subalgebra of this algebracontains half of the Kac-Moody Lie algebra associated to the real subquiver of$Q$.  Lifting $\mathfrak{g}_{\Pi_Q}$ to a Lie algebra in the category of mixedHodge modules on the coarse moduli space of $\Pi_Q$-modules, we prove that theintersection cohomology of spaces of semistable $\Pi_Q$-modules provide"cuspidal cohomology" for $\mathfrak{g}_{\Pi_Q}$ - a conjecturally completespace of simple hyperbolic roots for this Lie algebra.

BPS Lie algebras and the less perverse filtration on the preprojective CoHA