On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917070471430144 |
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| author | Matsumoto, Kengo Sogabe, Taro |
| author_facet | Matsumoto, Kengo Sogabe, Taro |
| contents | Reciprocality in Kirchberg algebras with finitely generated K-groups is regarded as a K-theoretic duality through K-groups and strong extension groups. We will prove that the reciprocal Kirchberg algebra has a universal property with respect to some generating C*-subalgebra and a family of generating partial isometries. By using the universal property, we will prove that there exists an aperiodic ergodic automorphism on an arbitrary unital Kirchberg algebra with finitely generated K-groups, which has a unique invariant state. The state is pure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06760 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms Matsumoto, Kengo Sogabe, Taro Operator Algebras Reciprocality in Kirchberg algebras with finitely generated K-groups is regarded as a K-theoretic duality through K-groups and strong extension groups. We will prove that the reciprocal Kirchberg algebra has a universal property with respect to some generating C*-subalgebra and a family of generating partial isometries. By using the universal property, we will prove that there exists an aperiodic ergodic automorphism on an arbitrary unital Kirchberg algebra with finitely generated K-groups, which has a unique invariant state. The state is pure. |
| title | On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2511.06760 |