Continuous categories of endomorphisms associated with $G$-kernels
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911692091293696 |
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| author | Bischoff, Marcel Karmakar, Pradyut |
| author_facet | Bischoff, Marcel Karmakar, Pradyut |
| contents | We generalize the construction of tensor categories of endomorphisms of a type III factor $M$ associated with a $G$-kernel, from the case of a discrete group $G$ to that of a compact second countable group. Our approach is based on the construction of a unitary tensor functor from a category of $C(G)$-modules to the category of endomorphisms of $M$. This functor maps a $C(G)$-module, realized as the space of square-integrable functions on a measure space, to a continuous family of endomorphisms of $M$. The resulting structure is a continuous category of endomorphisms, which provides a new framework for studying the interplay between subfactor theory and the representation theory of continuous groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Continuous categories of endomorphisms associated with $G$-kernels Bischoff, Marcel Karmakar, Pradyut Operator Algebras Mathematical Physics Category Theory Functional Analysis Quantum Algebra We generalize the construction of tensor categories of endomorphisms of a type III factor $M$ associated with a $G$-kernel, from the case of a discrete group $G$ to that of a compact second countable group. Our approach is based on the construction of a unitary tensor functor from a category of $C(G)$-modules to the category of endomorphisms of $M$. This functor maps a $C(G)$-module, realized as the space of square-integrable functions on a measure space, to a continuous family of endomorphisms of $M$. The resulting structure is a continuous category of endomorphisms, which provides a new framework for studying the interplay between subfactor theory and the representation theory of continuous groups. |
| title | Continuous categories of endomorphisms associated with $G$-kernels |
| topic | Operator Algebras Mathematical Physics Category Theory Functional Analysis Quantum Algebra |
| url | https://arxiv.org/abs/2605.17514 |