C$^*$-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912263856717824 |
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| author | Raad, Ali Imad |
| author_facet | Raad, Ali Imad |
| contents | We associate a Bratteli-type diagram to AH-algebras arising from generalized diagonal connecting maps. We use this diagram to give an explicit description of the connected components of the spectrum of an associated canonical C$^*$-diagonal. We introduce a topological notion on these connected components, that of being spectrally incomplete, and use it as a tool to show how various classes of AI-algebras, including certain Goodearl algebras and AH-algebra models for dynamical systems $([0,1],σ)$, do not admit unique inductive limit Cartan subalgebras. We focus on a class of spectrally complete C$^*$-algebras, namely the AF-algebras, and discuss the uniqueness of their inductive limit Cartan subalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_16707 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | C$^*$-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness Raad, Ali Imad Operator Algebras Functional Analysis 46L05 (Primary), 22A22 (Secondary) We associate a Bratteli-type diagram to AH-algebras arising from generalized diagonal connecting maps. We use this diagram to give an explicit description of the connected components of the spectrum of an associated canonical C$^*$-diagonal. We introduce a topological notion on these connected components, that of being spectrally incomplete, and use it as a tool to show how various classes of AI-algebras, including certain Goodearl algebras and AH-algebra models for dynamical systems $([0,1],σ)$, do not admit unique inductive limit Cartan subalgebras. We focus on a class of spectrally complete C$^*$-algebras, namely the AF-algebras, and discuss the uniqueness of their inductive limit Cartan subalgebras. |
| title | C$^*$-diagonals in AH-algebras arising from generalized diagonal connecting maps: spectrum and uniqueness |
| topic | Operator Algebras Functional Analysis 46L05 (Primary), 22A22 (Secondary) |
| url | https://arxiv.org/abs/2303.16707 |