Affine BPS algebras, W algebras, and the cohomological Hall algebra of 𝔸²

Source abstract

We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with its canonical cubic potential, and use them to precisely determine the T T -equivariant cohomological Hall algebra A A 2 T \mathcal {A}_{\mathbb {A}^{2}}^{T} of compactly supported coherent sheaves on A C 2 \mathbb {A}_{\mathbb {C}}^{2} , acted on by a torus T T . In particular we show that this algebra is spherically generated for all T T .