On localizing subcategories of Lie superalgebra representations
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915202968059904 |
|---|---|
| author | Hamil, Matthew H. |
| author_facet | Hamil, Matthew H. |
| contents | We state and prove a stratification result that allows us to classify the tensor ideal localizing subcategories for the stable module category $\text{Stab}(\mathcal{C}_{(\mathfrak{g}, \mathfrak{g}_{\bar 0})})$ of Lie superalgbera representations which are semisimple as representations of $\mathfrak{g}_{\bar 0}$ under the hypotheses that $\mathfrak{g}$ is a classical Lie superalgebra with a splitting detecting subalgebra $\mathfrak{z} \leq \mathfrak{g}$, as well as a natural hypothesis on realization of supports. This extends the work of the author and Nakano where a similar classification was obtained for the stable category of modules over a detecting subalgebra employing stratification in the sense of Benson, Iyengar, and Krause. Our new result involves making use of a more general stratification framework in weakly Noetherian contexts developed by Barthel, Heard, and Sanders using the Balmer-Favi notion of support for big objects in tensor triangulated categories, as well as the recently developed homological stratification of Barthel, Heard, Sanders, and Zou in using the homological spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13639 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On localizing subcategories of Lie superalgebra representations Hamil, Matthew H. Representation Theory We state and prove a stratification result that allows us to classify the tensor ideal localizing subcategories for the stable module category $\text{Stab}(\mathcal{C}_{(\mathfrak{g}, \mathfrak{g}_{\bar 0})})$ of Lie superalgbera representations which are semisimple as representations of $\mathfrak{g}_{\bar 0}$ under the hypotheses that $\mathfrak{g}$ is a classical Lie superalgebra with a splitting detecting subalgebra $\mathfrak{z} \leq \mathfrak{g}$, as well as a natural hypothesis on realization of supports. This extends the work of the author and Nakano where a similar classification was obtained for the stable category of modules over a detecting subalgebra employing stratification in the sense of Benson, Iyengar, and Krause. Our new result involves making use of a more general stratification framework in weakly Noetherian contexts developed by Barthel, Heard, and Sanders using the Balmer-Favi notion of support for big objects in tensor triangulated categories, as well as the recently developed homological stratification of Barthel, Heard, Sanders, and Zou in using the homological spectrum. |
| title | On localizing subcategories of Lie superalgebra representations |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2503.13639 |