Groupoid homology and K-theory for algebraic actions from number theory
Operator Algebras
2024-07-03 v1 Algebraic Topology
Dynamical Systems
K-Theory and Homology
Number Theory
Abstract
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 L\"uck 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.
Cite
@article{arxiv.2407.01952,
title = {Groupoid homology and K-theory for algebraic actions from number theory},
author = {Chris Bruce and Yosuke Kubota and Takuya Takeishi},
journal= {arXiv preprint arXiv:2407.01952},
year = {2024}
}
Comments
38 pages