Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866914912991707136 |
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| author | Fletcher, James Gillaspy, Elizabeth Sims, Aidan |
| author_facet | Fletcher, James Gillaspy, Elizabeth Sims, Aidan |
| contents | We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph C*-algebra is independent of the factorisation rules, and we further show that the K-theory of any twisted k-graph C*-algebra is independent of the twisting 2-cocycle. We also explore applications to K-theory for the C*-algebras of single-vertex k-graphs, reducing the question of whether the $K$-theory is independent of the factorisation rules to a question about path-connectedness of the space of solutions to an equation of Yang-Baxter type. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_00959 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras Fletcher, James Gillaspy, Elizabeth Sims, Aidan Operator Algebras 46L05 We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph C*-algebra is independent of the factorisation rules, and we further show that the K-theory of any twisted k-graph C*-algebra is independent of the twisting 2-cocycle. We also explore applications to K-theory for the C*-algebras of single-vertex k-graphs, reducing the question of whether the $K$-theory is independent of the factorisation rules to a question about path-connectedness of the space of solutions to an equation of Yang-Baxter type. |
| title | Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras |
| topic | Operator Algebras 46L05 |
| url | https://arxiv.org/abs/1911.00959 |