Admissibility of C*-Covers for Operator Algebra Dynamical Systems
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911809670217728 |
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| author | Hamidi, Mitch |
| author_facet | Hamidi, Mitch |
| contents | We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such an extension form a complete lattice. We study dynamical systems arising from groups acting via inner automorphisms in a C*-cover and produce an example of a C*-cover that admits no extension of dynamics on a finite-dimensional non-self-adjoint operator algebra. We construct a partial action on a class of C*-covers that recovers the crossed product of an operator algebra as a subalgebra of the partial crossed product, even when the C*-cover admits no dynamical extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Admissibility of C*-Covers for Operator Algebra Dynamical Systems Hamidi, Mitch Operator Algebras 47L55, 46L55, 47L65 We characterize when a C*-cover admits a C*-dynamical extension of dynamics on an operator algebra in terms of the boundary ideal structure for the operator algebra in its maximal representation and show that the C*-covers that admit such an extension form a complete lattice. We study dynamical systems arising from groups acting via inner automorphisms in a C*-cover and produce an example of a C*-cover that admits no extension of dynamics on a finite-dimensional non-self-adjoint operator algebra. We construct a partial action on a class of C*-covers that recovers the crossed product of an operator algebra as a subalgebra of the partial crossed product, even when the C*-cover admits no dynamical extension. |
| title | Admissibility of C*-Covers for Operator Algebra Dynamical Systems |
| topic | Operator Algebras 47L55, 46L55, 47L65 |
| url | https://arxiv.org/abs/2403.15349 |