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arXiv · 2511.09991

Properly Outer Actions of Tensor Categories on C$^*$-algebras

Roberto Hernández Palomares·Miho Mukohara
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Abstract

We discuss proper outerness for finite index endomorphisms and finite index bimodules of simple C$^*$-algebras, extending recent similar results by Izumi concerning the purely infinite setting. Our main result is that proper outerness holds automatically for finite index outer endomorphisms of simple C$^*$-algebras. Consequently, freeness for outer actions of unitary tensor categories on simple C$^*$-algebras is also shown to hold automatically. As applications, we obtain structural results about potentially infinite index irreducible discrete inclusions of C$^*$-algebras, such as C$^*$-irreducibility.

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Roberto Hernández Palomares, Miho Mukohara. 2025-11-13. Properly Outer Actions of Tensor Categories on C$^*$-algebras. https://doi.org/10.1007/s00220-026-05665-7

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