Modules over the category of Jacobi diagrams in handlebodies

Mai Katada

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arXiv · 2509.16230

Modules over the category of Jacobi diagrams in handlebodies

Mai Katada

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Abstract

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 $\mathbf{A}(0,-)$.

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BibTeX RIS

Mai Katada. 2025-09-14. Modules over the category of Jacobi diagrams in handlebodies. https://arxiv.org/abs/2509.16230

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