Towards interpolating categories for equivariant map algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908343719690240 |
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| author | Samchuck-Schnarch, Saima |
| author_facet | Samchuck-Schnarch, Saima |
| contents | Using the language of string diagrams, we define categorical generalizations of modules for map algebras $\mathfrak{g} \otimes A$ and equivariant map algebras $(\mathfrak{g} \otimes A)^Γ$, where $\mathfrak{g}$ is a Lie algebra, $A$ is a commutative associative algebra, and $Γ$ is an abelian group acting on $\mathfrak{g}$ and $A$. After establishing some properties of these modules, we present several examples of how our definitions can applied in various diagrammatic categories. In particular, we use the oriented Brauer category OB to construct a candidate interpolating category for the categories of $\mathfrak{gl}_n \otimes k[t]$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21163 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards interpolating categories for equivariant map algebras Samchuck-Schnarch, Saima Representation Theory Category Theory 18M30, 18M05, 17B10 Using the language of string diagrams, we define categorical generalizations of modules for map algebras $\mathfrak{g} \otimes A$ and equivariant map algebras $(\mathfrak{g} \otimes A)^Γ$, where $\mathfrak{g}$ is a Lie algebra, $A$ is a commutative associative algebra, and $Γ$ is an abelian group acting on $\mathfrak{g}$ and $A$. After establishing some properties of these modules, we present several examples of how our definitions can applied in various diagrammatic categories. In particular, we use the oriented Brauer category OB to construct a candidate interpolating category for the categories of $\mathfrak{gl}_n \otimes k[t]$-modules. |
| title | Towards interpolating categories for equivariant map algebras |
| topic | Representation Theory Category Theory 18M30, 18M05, 17B10 |
| url | https://arxiv.org/abs/2504.21163 |