Extensions between functors from Jacobi diagrams in handlebodies
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914087397490688 |
|---|---|
| author | Katada, Mai |
| author_facet | Katada, Mai |
| contents | The first Ext-groups between Schur functors in the category of modules over the $\Bbbk$-linearization $\Bbbk\mathbf{gr}^{\operatorname{op}}$ of the opposite of the category of finitely generated free groups are computed for a filed $\Bbbk$ of characteristic $0$. The $\Bbbk$-linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies, which was introduced by Habiro and Massuyeau, has an $\mathbb{N}$-grading whose degree $0$ part identifies with the category $\Bbbk\mathbf{gr}^{\operatorname{op}}$. We compute the first Ext-groups in the category of $\mathbf{A}$-modules between simple $\mathbf{A}$-modules which are induced by Schur functors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions between functors from Jacobi diagrams in handlebodies Katada, Mai Category Theory Algebraic Topology Quantum Algebra 18A25, 18A40, 18G15, 57K16 The first Ext-groups between Schur functors in the category of modules over the $\Bbbk$-linearization $\Bbbk\mathbf{gr}^{\operatorname{op}}$ of the opposite of the category of finitely generated free groups are computed for a filed $\Bbbk$ of characteristic $0$. The $\Bbbk$-linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies, which was introduced by Habiro and Massuyeau, has an $\mathbb{N}$-grading whose degree $0$ part identifies with the category $\Bbbk\mathbf{gr}^{\operatorname{op}}$. We compute the first Ext-groups in the category of $\mathbf{A}$-modules between simple $\mathbf{A}$-modules which are induced by Schur functors. |
| title | Extensions between functors from Jacobi diagrams in handlebodies |
| topic | Category Theory Algebraic Topology Quantum Algebra 18A25, 18A40, 18G15, 57K16 |
| url | https://arxiv.org/abs/2510.09625 |