http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:79 We prove a symmetric imprimitivity theorem for commuting proper actions of locally compact groups H and K on a C*-algebra. 2010-07-23T04:06:00.731Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:62 Given a k-graph Lambda and an element p of N-k, we define the dual k-graph, p Lambda. We show that when Lambda is row-finite and has no sources, the C*-algebras C*(Lambda) and C*(p Lambda) coincide. We use this isomorphism to apply Robertson and Steger's results to calculate the K-theory of C*(Lambda) when Lambda is finite and strongly connected and satisfies the aperiodicity condition. 2010-07-23T03:30:03.124Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:424 There has recently been much interest in the C*-algebras of directed graphs. Here we consider product systems E of directed graphs over sernigroups and associated C*-algebras C* (E) and TC* (E) which generalise the higher-rank graph algebras of Kumjian-Pask and their Toeplitz analogues. We study these algebras by constructing from E a product system X(E) of Hilbert bimodules, and applying recent results of Fowler about the Toeplitz algebras of such systems. Fowler's hypotheses turn out to be very interesting graph-theoretically, and indicate new relations which will have to be added to the usual Cuntz-Krieger relations to obtain a satisfactory theory of Cuntz-Krieger algebras for product systems of graphs; our algebras C* (E) and TC* (E) are universal for families of partial isometries satisfying these relations. Our main result is a uniqueness theorem for TC*(E) which has particularly interesting implications for the C*-algebras of non-row-finite higher-rank graphs. This theorem is apparently beyond the reach of Fowler's theory, and our proof requires a detailed analysis of the expectation onto the diagonal in TC*(E). 2010-06-11T02:14:20.219Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:420 k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop the theory of covering spaces for k-graphs, obtaining a satisfactory version of the usual topological classification in terms of subgroups of a fundamental group. We then use this classification to describe the C*-algebras of covering k-graphs as crossed products by coactions of homogeneous spaces, generalizing recent results on the C*-algebras of graphs. 2010-06-03T06:10:34.648Z ]]>