Subcategories of Module Categories via Restricted Yoneda Embeddings
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908454100140032 |
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| author | Fillmore, Dylan Hartwig, Jonas T. |
| author_facet | Fillmore, Dylan Hartwig, Jonas T. |
| contents | We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda embedding of ${}_A\mathsf{Mod}$ with a restriction to certain subcategories $\mathcal{B}\subset {}_A\mathsf{Mod}$, typically consisting of cyclic modules. We describe the subcategories on which $Y$ provides an equivalence of categories. This also provides a way to understand the subcategories of ${}_A\mathsf{Mod}$ that arise this way. Many well-known categories are obtained in this way, including categories of weight modules and Harish-Chandra modules with respect to a subalgebra $Γ$ of $A$. In other special cases the equivalence involves modules over the Mickelsson step algebra associated to a reductive pair of Lie algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Subcategories of Module Categories via Restricted Yoneda Embeddings Fillmore, Dylan Hartwig, Jonas T. Representation Theory We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda embedding of ${}_A\mathsf{Mod}$ with a restriction to certain subcategories $\mathcal{B}\subset {}_A\mathsf{Mod}$, typically consisting of cyclic modules. We describe the subcategories on which $Y$ provides an equivalence of categories. This also provides a way to understand the subcategories of ${}_A\mathsf{Mod}$ that arise this way. Many well-known categories are obtained in this way, including categories of weight modules and Harish-Chandra modules with respect to a subalgebra $Γ$ of $A$. In other special cases the equivalence involves modules over the Mickelsson step algebra associated to a reductive pair of Lie algebras. |
| title | Subcategories of Module Categories via Restricted Yoneda Embeddings |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2507.12778 |