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arXiv · 2504.05247

Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility

Lucas Hataishi·Roberto Hernández Palomares
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Abstract

We derive faithful inclusions of C*-algebras from a coend-type construction in unitary tensor categories. This gives rise to different potential notions of discreteness for an inclusion in the non-irreducible case, and provides a unified framework that encloses the theory of compact quantum group actions. We also provide examples coming from semi-circular systems and from factorization homology. In the irreducible case, we establish conditions under which the C*-discrete and W*-discrete conditions are equivalent.

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Lucas Hataishi, Roberto Hernández Palomares. 2025-04-07. Inclusions of Operator Algebras from Tensor Categories: beyond irreducibility. https://doi.org/10.1017/s0017089525100839

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