Kaydedildi:
| Asıl Yazarlar: | , , |
|---|---|
| Materyal Türü: | Preprint |
| Baskı/Yayın Bilgisi: |
2020
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| Konular: | |
| Online Erişim: | https://arxiv.org/abs/2012.05561 |
| Etiketler: |
Etiketle
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İçindekiler:
- 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.