Weyl group actions on quiver varieties

In this talk, I will present a construction of Weyl group actions on the cohomology of quiver varieties coming out of the description of the BPS cohomology of the preprojective algebra of a quiver as a positive generalized Kac--Moody Lie algebra. I will explain consequences regarding generation of BPS cohomology of preprojective algebras. This is based on joint work with Ben Davison.