Classification theorems for the C*-algebras of graphs with sinks

We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors W_E : G^0 -> N which describe how the sinks are attached to G; more precisely, the invariants are the classes of the W_E in the cokernel of the map A-I, where A is the adjacency matrix of the graph G.Comment: 16 pages, uses XY-pi

Induction in stages for crossed products of C*-algebras by maximal coactions

Let B be a C*-algebra with a maximal coaction of a locally compact group G, and let N and H be closed normal subgroups of G with N contained in H. We show that the process Ind_(G/H)^G which uses Mansfield's bimodule to induce representations of the crossed product of B by G from those of the restricted crossed product of B by (G/H) is equivalent to the two-stage induction process: Ind_(G/N)^G composed with Ind_(G/H)^(G/N). The proof involves a calculus of symmetric imprimitivity bimodules which relates the bimodule tensor product to the fibred product of the underlying spaces.Comment: 38 pages, LaTeX, uses Xy-pic; significant reorganization of previous version; short section on regularity of induced representations adde

Full and reduced coactions of locally compact groups on C*-algebras

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we use definitions and constructions that are well-documented and accessible to non-experts, and otherwise we provide full details. We then give a series of applications to illustrate the use of these techniques. We obtain in particular a new version of Mansfield's imprimitivity theorem for full coactions, and prove that it gives a natural isomorphism between crossed-product functors defined on appropriate categories

Moore Cohomology, Principal Bundles, and Actions of Groups on c*-algebras

In recent years both topological and algebraic invariants have been associated to group actions on C*-algebras. Principal bundles have been used to describe the topological structure of the spectrum of crossed products [18, 19], and as a result we now know that crossed products of even the very nicest non-commutative algebras can be substantially more complicated than those of commutative algebras [19, 5]. The algebraic approach involves group cohomological invariants, and exploits the associated machinery to classify group actions on C*-algebras; this originated in [2], and has been particularly successful for actions of R and tori ([19; Section 4], [21]). Here we shall look in detail at the relationship between these topological and algebraic invariants, with a view to analyzing the structure of the systems studied in [19; Section 2, 3]