Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\mathbb{A}^2$
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912483274391552 |
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| author | Davison, Ben |
| author_facet | Davison, Ben |
| contents | We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with potential, and use them to precisely 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 this algebra is spherically generated for all $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05971 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\mathbb{A}^2$ Davison, Ben Representation Theory High Energy Physics - Theory Algebraic Geometry We introduce affinizations and deformations of the BPS Lie algebra associated to a tripled quiver with potential, and use them to precisely 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 this algebra is spherically generated for all $T$. |
| title | Affine BPS algebras, W algebras, and the cohomological Hall algebra of $\mathbb{A}^2$ |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2209.05971 |