Groupoid homology and K-theory for algebraic actions from number theory
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909238656237568 |
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| author | Bruce, Chris Kubota, Yosuke Takeishi, Takuya |
| author_facet | Bruce, Chris Kubota, Yosuke Takeishi, Takuya |
| contents | We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homology of the topological full groups associated with rings of algebraic integers, and we use our groupoid homology calculation to compute the K-theory for ring C*-algebras of rings of algebraic integers, recovering the results of Cuntz and Li and of Li and Lück without using Cuntz--Li duality. Moreover, we compute the K-theory for C*-algebras attached to integral dynamics, resolving the conjecture by Barlak, Omland, and Stammeier in full generality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Groupoid homology and K-theory for algebraic actions from number theory Bruce, Chris Kubota, Yosuke Takeishi, Takuya Operator Algebras Algebraic Topology Dynamical Systems K-Theory and Homology Number Theory Primary 46L80, 22A22, Secondary 37A55, 11R04 We compute the groupoid homology for the ample groupoids associated with algebraic actions from rings of algebraic integers and integral dynamics. We derive results for the homology of the topological full groups associated with rings of algebraic integers, and we use our groupoid homology calculation to compute the K-theory for ring C*-algebras of rings of algebraic integers, recovering the results of Cuntz and Li and of Li and Lück without using Cuntz--Li duality. Moreover, we compute the K-theory for C*-algebras attached to integral dynamics, resolving the conjecture by Barlak, Omland, and Stammeier in full generality. |
| title | Groupoid homology and K-theory for algebraic actions from number theory |
| topic | Operator Algebras Algebraic Topology Dynamical Systems K-Theory and Homology Number Theory Primary 46L80, 22A22, Secondary 37A55, 11R04 |
| url | https://arxiv.org/abs/2407.01952 |