C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory
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arXiv
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| Format: | Preprint |
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2020
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| author | Mutter, Sam A. Radu, Aura-Cristiana Vdovina, Alina |
| author_facet | Mutter, Sam A. Radu, Aura-Cristiana Vdovina, Alina |
| contents | We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph. We make deductions about the K-theory of the corresponding $k$-rank graph C*-algebras, and give explicit examples of $k$-cube groups and their K-theory. We give explicit computations of K-theory for an infinite family of $k$-rank graphs for $k\geq 3$, which is not a direct consequence of the Künneth Theorem for tensor products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_05561 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory Mutter, Sam A. Radu, Aura-Cristiana Vdovina, Alina Operator Algebras Group Theory 46L80, 20E08 We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action on the product of trees defines a $k$-dimensional cube complex, which induces a higher-rank graph. We make deductions about the K-theory of the corresponding $k$-rank graph C*-algebras, and give explicit examples of $k$-cube groups and their K-theory. We give explicit computations of K-theory for an infinite family of $k$-rank graphs for $k\geq 3$, which is not a direct consequence of the Künneth Theorem for tensor products. |
| title | C*-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their K-theory |
| topic | Operator Algebras Group Theory 46L80, 20E08 |
| url | https://arxiv.org/abs/2012.05561 |