Continuous categories of endomorphisms associated with $G$-kernels

Marcel Bischoff; Pradyut Karmakar

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arXiv · 2605.17514

Continuous categories of endomorphisms associated with $G$-kernels

Marcel Bischoff·Pradyut Karmakar

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Abstract

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.

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BibTeX RIS

Marcel Bischoff, Pradyut Karmakar. 2026-05-17. Continuous categories of endomorphisms associated with $G$-kernels. https://arxiv.org/abs/2605.17514

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