Computable $K$-theory for C*-algebras II: AF algebras
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915780547837952 |
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| author | Eagle, Christopher J. Goldbring, Isaac McNicholl, Timothy H. |
| author_facet | Eagle, Christopher J. Goldbring, Isaac McNicholl, Timothy H. |
| contents | We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive limit of finite-dimensional algebras. Using this, and an analogous result for dimension groups, we show that the computable $K_0$ functor provides a computable equivalence of categories between c.e. presentations of AF algebras and c.e. presentations of unital (scaled) dimension groups, giving an effective version of Elliott's classification theorem. We use our results to determine the complexity of the index set and isomorphism problems for various classes of AF algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06882 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computable $K$-theory for C*-algebras II: AF algebras Eagle, Christopher J. Goldbring, Isaac McNicholl, Timothy H. Operator Algebras Logic We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive limit of finite-dimensional algebras. Using this, and an analogous result for dimension groups, we show that the computable $K_0$ functor provides a computable equivalence of categories between c.e. presentations of AF algebras and c.e. presentations of unital (scaled) dimension groups, giving an effective version of Elliott's classification theorem. We use our results to determine the complexity of the index set and isomorphism problems for various classes of AF algebras. |
| title | Computable $K$-theory for C*-algebras II: AF algebras |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2602.06882 |