Properly Outer Actions of Tensor Categories on C$^*$-algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911609861963776 |
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| author | Palomares, Roberto Hernández Mukohara, Miho |
| author_facet | Palomares, Roberto Hernández Mukohara, Miho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properly Outer Actions of Tensor Categories on C$^*$-algebras Palomares, Roberto Hernández Mukohara, Miho Operator Algebras 46L05(Primary), 46L08, 46L55, 46M15 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. |
| title | Properly Outer Actions of Tensor Categories on C$^*$-algebras |
| topic | Operator Algebras 46L05(Primary), 46L08, 46L55, 46M15 |
| url | https://arxiv.org/abs/2511.09991 |