Abstract

A covering of kgraphs (in the sense of PaskQuigg
Raeburn) induces an embedding of universal Calgebras. We show
how to build a (k+1)graph whose universal algebra encodes this
embedding. More generally we show how to realise a direct limit
of kgraph algebras under embeddings induced from coverings as the
universal algebra of a (k+1)graph. Our main focus is on computing
the Ktheory of the (k+1)graph algebra from that of the component
kgraph algebras.
Examples of our construction include a realisation of the Kirchberg
algebra P_n whose Ktheory is opposite to that of O_n, and a class of
ATalgebras that can naturally be regarded as higherrank Bunce
Deddens algebras.