@TECHREPORT{Evans02onhigher, author = {D. Gwion Evans}, title = {On higher rank graph C ∗ -algebras}, institution = {}, year = {2002} }

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Abstract

Abstract. Given a row-finite k-graph Λ with no sources we investigate the K-theory of the higher rank graph C ∗-algebra, C ∗ (Λ). When k = 2 we are able to give explicit formulae to calculate the K-groups of C ∗ (Λ). The K-groups of C ∗ (Λ) for k> 2 can be calculated under certain circumstances. We state that for all k, the torsion-free rank of K0(C ∗ (Λ)) and K1(C ∗ (Λ)) are equal when C ∗ (Λ) is unital, and we determine the position of the class of the unit of C ∗ (Λ) in K0(C ∗ (Λ)). 1.