A C*-cover lattice dichotomy
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909984947699712 |
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| author | Humeniuk, Adam Ramsey, Christopher Scherer, Marcel |
| author_facet | Humeniuk, Adam Ramsey, Christopher Scherer, Marcel |
| contents | In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator algebras with a one-point lattice in two ways: as an explicit subalgebra of the C*-algebra of a universal contraction, and via a direct limit construction inspired by the work of Kirchberg and Wassermann for operator systems. We also establish that the C*-envelope need not have an immediate successor C*-cover in the lattice, and that a semi-Dirichlet non-selfadjoint operator algebra never has a one-point lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A C*-cover lattice dichotomy Humeniuk, Adam Ramsey, Christopher Scherer, Marcel Operator Algebras In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator algebras with a one-point lattice in two ways: as an explicit subalgebra of the C*-algebra of a universal contraction, and via a direct limit construction inspired by the work of Kirchberg and Wassermann for operator systems. We also establish that the C*-envelope need not have an immediate successor C*-cover in the lattice, and that a semi-Dirichlet non-selfadjoint operator algebra never has a one-point lattice. |
| title | A C*-cover lattice dichotomy |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2601.05088 |