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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.18161 |
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| _version_ | 1866917541048221696 |
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| author | Palomares, Roberto Hernández Nelson, Brent |
| author_facet | Palomares, Roberto Hernández Nelson, Brent |
| contents | We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality condition. Furthermore, we define freeness for actions of tensor categories on C*-algebras, and show simplicity is preserved under taking reduced crossed products. Finally, we show under certain constraints that A-valued semicircular systems give rise to C*-discrete inclusions, and thus are crossed products by an action of a tensor category. Along the way, we show the set of single algebraic generators of a dualizable bimodule forms an open subset. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remarks on C*-discrete inclusions Palomares, Roberto Hernández Nelson, Brent Operator Algebras We obtain a Galois correspondence between the lattice of intermediate C*-discrete subalgebras intermediate to a given irreducible C*-discrete inclusion, and characterize these as targets of compatible expectations under a traciality condition. Furthermore, we define freeness for actions of tensor categories on C*-algebras, and show simplicity is preserved under taking reduced crossed products. Finally, we show under certain constraints that A-valued semicircular systems give rise to C*-discrete inclusions, and thus are crossed products by an action of a tensor category. Along the way, we show the set of single algebraic generators of a dualizable bimodule forms an open subset. |
| title | Remarks on C*-discrete inclusions |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2409.18161 |