Modules over the category of Jacobi diagrams in handlebodies
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912595171082240 |
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| author | Katada, Mai |
| author_facet | Katada, Mai |
| contents | The linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies was introduced by Habiro and Massuyeau. We study the category of modules over the category $\mathbf{A}$. We generalize the adjunction given by Powell to an adjunction between the category of $\mathbf{A}$-modules and the category of modules over the linear PROP for Casimir Lie algebras by using the category $\mathbf{A}^{L}$ of extended Jacobi diagrams in handlebodies. Then we study subquotient $\mathbf{A}$-modules of $\mathbf{A}(0,-)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modules over the category of Jacobi diagrams in handlebodies Katada, Mai Representation Theory Algebraic Topology Geometric Topology Quantum Algebra 18A25, 18A40, 57K16, 18M85, 20F28 The linear category $\mathbf{A}$ of Jacobi diagrams in handlebodies was introduced by Habiro and Massuyeau. We study the category of modules over the category $\mathbf{A}$. We generalize the adjunction given by Powell to an adjunction between the category of $\mathbf{A}$-modules and the category of modules over the linear PROP for Casimir Lie algebras by using the category $\mathbf{A}^{L}$ of extended Jacobi diagrams in handlebodies. Then we study subquotient $\mathbf{A}$-modules of $\mathbf{A}(0,-)$. |
| title | Modules over the category of Jacobi diagrams in handlebodies |
| topic | Representation Theory Algebraic Topology Geometric Topology Quantum Algebra 18A25, 18A40, 57K16, 18M85, 20F28 |
| url | https://arxiv.org/abs/2509.16230 |