 

D. Gwion Evans
On the Ktheory of higher rank graph C*algebras


Published: 
January 22, 2008

Keywords: 
Ktheory, C*algebra, kgraphs, graph algebra 
Subject: 
Primary 46L80; Secondary 46L35 


Abstract
Given a rowfinite kgraph Λ with no sources we
investigate the Ktheory of the higher rank graph C*algebra, C*(Λ). When k=2 we are able to give explicit
formulae to calculate the Kgroups of C*(Λ). The Kgroups 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
torsionfree rank of K_{0}(C*(Λ)) and K_{1}(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 K_{0}(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

