Infinite-Dimensional Towers and a Categorification of Differential Operators on $\mathbb{A}^1_{\mathbb{Z}[v,v^{- 1}]}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908556717981696 |
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| author | Lai, Chun-Ju Li, Cailan |
| author_facet | Lai, Chun-Ju Li, Cailan |
| contents | We introduce axioms for towers of infinite-dimensional algebras such that the corresponding Grothendieck groups of projective and finite-dimensional modules are Hopf dual to each other. This duality gives rise to an action of the Hesienberg double -- a generalization of the classical Hesienberg algebra -- on the Grothendieck group. We categorify this action and, as an application, construct a categorical realization of quantum differential operators on $\mathbb{A}^1_{\mathbb{Z}[v,v^{-1}]}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite-Dimensional Towers and a Categorification of Differential Operators on $\mathbb{A}^1_{\mathbb{Z}[v,v^{- 1}]}$ Lai, Chun-Ju Li, Cailan Representation Theory We introduce axioms for towers of infinite-dimensional algebras such that the corresponding Grothendieck groups of projective and finite-dimensional modules are Hopf dual to each other. This duality gives rise to an action of the Hesienberg double -- a generalization of the classical Hesienberg algebra -- on the Grothendieck group. We categorify this action and, as an application, construct a categorical realization of quantum differential operators on $\mathbb{A}^1_{\mathbb{Z}[v,v^{-1}]}$. |
| title | Infinite-Dimensional Towers and a Categorification of Differential Operators on $\mathbb{A}^1_{\mathbb{Z}[v,v^{- 1}]}$ |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2509.20053 |