K-theory of C*-algebras arising from commuting Hilbert bimodules and invariant ideals
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| Format: | Preprint |
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2025
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| _version_ | 1866914001409015808 |
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| author | Huef, Astrid an Ng, Abraham C. S. Sims, Aidan |
| author_facet | Huef, Astrid an Ng, Abraham C. S. Sims, Aidan |
| contents | We study the K-theory of the Cuntz-Nica-Pimsner C*-algebra of a rank-two product system that is an extension determined by an invariant ideal of the coefficient algebra. We use a construction of Deaconu and Fletcher that describes the Cuntz-Nica-Pimsner C*-algebra of the product system in terms of two iterations of Pimsner's original construction of a C*-algebra from a right-Hilbert bimodule. We apply our results to the product system built from two commuting surjective local homeomorphisms of a totally disconnected space, where the Cuntz-Nica-Pimsner C*-algebra is isomorphic to the C*-algebra of the associated rank-two Deaconu--Renault groupoid. We then apply a theorem of Spielberg about stable finiteness of an extension to obtain sufficient conditions for stable finiteness of the C*-algebra of the Deaconu-Renault groupoid. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_00377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | K-theory of C*-algebras arising from commuting Hilbert bimodules and invariant ideals Huef, Astrid an Ng, Abraham C. S. Sims, Aidan Operator Algebras 46L05 (primary), 46L55, 46L80 (secondary) We study the K-theory of the Cuntz-Nica-Pimsner C*-algebra of a rank-two product system that is an extension determined by an invariant ideal of the coefficient algebra. We use a construction of Deaconu and Fletcher that describes the Cuntz-Nica-Pimsner C*-algebra of the product system in terms of two iterations of Pimsner's original construction of a C*-algebra from a right-Hilbert bimodule. We apply our results to the product system built from two commuting surjective local homeomorphisms of a totally disconnected space, where the Cuntz-Nica-Pimsner C*-algebra is isomorphic to the C*-algebra of the associated rank-two Deaconu--Renault groupoid. We then apply a theorem of Spielberg about stable finiteness of an extension to obtain sufficient conditions for stable finiteness of the C*-algebra of the Deaconu-Renault groupoid. |
| title | K-theory of C*-algebras arising from commuting Hilbert bimodules and invariant ideals |
| topic | Operator Algebras 46L05 (primary), 46L55, 46L80 (secondary) |
| url | https://arxiv.org/abs/2504.00377 |