New York Journal of Mathematics Volume 14 (2008) 1-31
 Volume 14

D. Gwion Evans

On the K-theory of higher rank graph C*-algebras

 Published: January 22, 2008 Keywords: K-theory, C*-algebra, k-graphs, graph algebra Subject: Primary 46L80; Secondary 46L35

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 and we consider the case k=3. We prove that for arbitrary k, the torsion-free rank of K0(C*(Λ)) and K1(C*(Λ)) are equal when C*(Λ) is unital, and for k=2 we determine the position of the class of the unit of C*(Λ) in K0(C*(Λ)).

Acknowledgements

Research supported by the European Union Research Training Network in Quantum Spaces -- Noncommutative Geometry.

Author information

Institute of Mathematical and Physical Sciences, Aberystwyth University, Penglais Campus, Aberystwyth, Ceredigion, SY23 3BZ, Wales, UK
dfe@aber.ac.uk
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