# Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras

@article{Fletcher2019HomotopyOP,
title={Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras},
author={James Fletcher and Elizabeth A. Gillaspy and Aidan Sims},
journal={Indiana University Mathematics Journal},
year={2019}
}
• Published 3 November 2019
• Mathematics
• Indiana University Mathematics Journal
We introduce the notion of a homotopy of product systems, and show that the Cuntz-Nica-Pimsner algebras of homotopic product systems over N^k have isomorphic K-theory. As an application, we give a new proof that the K-theory of a 2-graph C*-algebra is independent of the factorisation rules, and we further show that the K-theory of any twisted k-graph C*-algebra is independent of the twisting 2-cocycle. We also explore applications to K-theory for the C*-algebras of single-vertex k-graphs…
1 Citations
We pose a conjecture on the K-theory of the self-similar $k$-graph C*-algebra of a standard product of odometers. We generalize the C*-algebra $\mathcal{Q}_S$ to any subset of \$\mathbb{N}^\times

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