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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2604.07698 |
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| _version_ | 1866908985452396544 |
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| author | Elliott, George A. Ruzicka, Vincent M. |
| author_facet | Elliott, George A. Ruzicka, Vincent M. |
| contents | We construct a ``noncommutative'' Villadsen algebra $B$ and show that, given an extreme tracial state $ν$ on its canonical AF subalgebra, the subset of $T(B)$ consisting of those tracial states that equal $ν$ when restricted to the canonical AF subalgebra is the Poulsen simplex. In particular, if the canonical AF subalgebra has a unique trace, then $T(B)$ is the Poulsen simplex. We go on to show that in certain instances, the tracial cone of a ``classical'' AF-Villadsen algebra $D$ is isomorphic to the tracial cone of the algebra obtained from $D$ by deleting all point evaluations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The trace simplex of a noncommutative Villadsen algebra Elliott, George A. Ruzicka, Vincent M. Operator Algebras We construct a ``noncommutative'' Villadsen algebra $B$ and show that, given an extreme tracial state $ν$ on its canonical AF subalgebra, the subset of $T(B)$ consisting of those tracial states that equal $ν$ when restricted to the canonical AF subalgebra is the Poulsen simplex. In particular, if the canonical AF subalgebra has a unique trace, then $T(B)$ is the Poulsen simplex. We go on to show that in certain instances, the tracial cone of a ``classical'' AF-Villadsen algebra $D$ is isomorphic to the tracial cone of the algebra obtained from $D$ by deleting all point evaluations. |
| title | The trace simplex of a noncommutative Villadsen algebra |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2604.07698 |