Vol. 7, No. 2, 2022

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$K\mkern-2mu$-theory for real $k$-graph $C^*$-algebras

Jeffrey L. Boersema and Elizabeth Gillaspy

Vol. 7 (2022), No. 2, 395–440
Abstract

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 K-theory of C(Λ,γ) for any involution γ on  Λ, and show that the E2 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 KCR(C (Λ,γ)) for several examples of higher-rank graphs Λ with involution.

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