A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917914121076736 |
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| author | Eryüzlü, Menevşe Tomforde, Mark |
| author_facet | Eryüzlü, Menevşe Tomforde, Mark |
| contents | We introduce a property of C*-correspondences, which we call Condition (S), to serve as an analogue of Condition (L) of graphs. We use Condition (S) to prove a Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner algebras and obtain sufficient conditions for simplicity of Cuntz-Pimsner algebras. We also prove that if Q is a topological quiver with no sinks and X(Q) is the associated C*-correspondence, then X(Q) satisfies Condition (S) if and only if Q satisfies Condition(L). Finally, we consider several examples to compare and contrast Condition (S) with Schweizer's nonperiodic condition. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_00248 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras Eryüzlü, Menevşe Tomforde, Mark Operator Algebras We introduce a property of C*-correspondences, which we call Condition (S), to serve as an analogue of Condition (L) of graphs. We use Condition (S) to prove a Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner algebras and obtain sufficient conditions for simplicity of Cuntz-Pimsner algebras. We also prove that if Q is a topological quiver with no sinks and X(Q) is the associated C*-correspondence, then X(Q) satisfies Condition (S) if and only if Q satisfies Condition(L). Finally, we consider several examples to compare and contrast Condition (S) with Schweizer's nonperiodic condition. |
| title | A Cuntz-Krieger Uniqueness Theorem for Cuntz-Pimsner Algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2212.00248 |