Couniversality for C*-algebras of residually finite-dimensional operator algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911059231637504 |
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| author | Humeniuk, Adam Ramsey, Christopher Thompson, Ian |
| author_facet | Humeniuk, Adam Ramsey, Christopher Thompson, Ian |
| contents | The C*-envelope of a non self-adjoint operator algebra is known to encode many properties of the underlying subalgebra. However, the C*-envelope does not always encode the residual finite-dimensionality of an operator algebra. To elucidate this failure, we study couniversal existence in the space of residually finite-dimensional (RFD) C*-algebras attached to a fixed operator algebra. We construct several examples of residually finite-dimensional operator algebras for which there does not exist a minimal RFD C*-algebra, answering a question of the first two authors. For large swathes of tensor algebras of C*-correspondences, we also prove that the space of RFD C*-algebras fails to be closed under infima of C*-covers. In the case of the disc algebra, we are able to achieve this failure for a single pair of RFD C*-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Couniversality for C*-algebras of residually finite-dimensional operator algebras Humeniuk, Adam Ramsey, Christopher Thompson, Ian Operator Algebras The C*-envelope of a non self-adjoint operator algebra is known to encode many properties of the underlying subalgebra. However, the C*-envelope does not always encode the residual finite-dimensionality of an operator algebra. To elucidate this failure, we study couniversal existence in the space of residually finite-dimensional (RFD) C*-algebras attached to a fixed operator algebra. We construct several examples of residually finite-dimensional operator algebras for which there does not exist a minimal RFD C*-algebra, answering a question of the first two authors. For large swathes of tensor algebras of C*-correspondences, we also prove that the space of RFD C*-algebras fails to be closed under infima of C*-covers. In the case of the disc algebra, we are able to achieve this failure for a single pair of RFD C*-algebras. |
| title | Couniversality for C*-algebras of residually finite-dimensional operator algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2507.11824 |