K-theory for real k-graph C∗-algebras

We initiate the study of real $C^{*}$ -algebras associated to higher-rank graphs $Λ$ , with a focus on their $K$ -theory. Following Kasparov and Evans, we identify a spectral sequence which computes the $𝒞 ℛ$ $K$ -theory of $C_{ℝ}^{*} (Λ, γ)$ for any involution $γ$ on $Λ$ , and show that the $E^{2}$ page of this spectral sequence can be straightforwardly computed from the combinatorial data of the $k$ -graph $Λ$ and the involution $γ$ . We provide a complete description of $K^{C R} (C_{ℝ}^{*} (Λ, γ))$ for several examples of higher-rank graphs $Λ$ with involution.

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Keywords

higher rank graphs, real $C^*$-algebras, $K\mkern-2mu$-theory

Mathematical Subject Classification

Primary: 46L80

Milestones

Received: 25 August 2021

Revised: 8 February 2022

Accepted: 24 February 2022

Published: 13 September 2022

Authors

Jeffrey L. Boersema
Mathematics Department Seattle University Seattle, WA United States

Elizabeth Gillaspy
Department of Mathematical Sciences University of Montana Missoula, MT United States

Vol. 7, No. 2, 2022

Jeffrey L. Boersema and Elizabeth Gillaspy

Abstract

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Keywords

Mathematical Subject Classification

Milestones

Authors