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# Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\mathbb{A}^2$

Sep 2022

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

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