120 research outputs found
Proper actions, fixed-point algebras and naturality in nonabelian duality
Suppose a locally compact group G acts freely and properly on a locally
compact Hausdorff space X, and let gamma be the induced action on C_0(X). We
consider a category in which the objects are C*-dynamical systems (A, G, alpha)
for which there is an equivariant homomorphism of (C_0(X), gamma) into the
multiplier algebra M(A). Rieffel has shown that such systems are proper and
saturated, and hence have a generalized fixed-point algebra A^alpha which is
Morita equivalent to A times_{alpha,r} G. We show that the assignment (A,
alpha) maps to A^alpha is functorial, and that Rieffel's Morita equivalence is
natural in a suitable sense. We then use our results to prove a categorical
version of Landstad duality which characterizes crossed products by coactions,
and to prove that Mansfield imprimitivity for crossed products by homogeneous
spaces is natural.Comment: 19 pages; minor revisio
Fundamental groupoids of k-graphs
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 a theory of the fundamental groupoid of a
k-graph, and relate it to the fundamental groupoid of an associated graph
called the 1-skeleton. We also explore the failure, in general, of k-graphs to
faithfully embed into their fundamental groupoids.Comment: 12 page
Making Photography Matter: A Viewer\u27s History from the Civil War to the Great Depression
Review of: "Making Photography Matter: A Viewer’s History from the Civil War to the Great Depression," by Cara A. Finnegan
Obstructions to a general characterization of graph correspondences
For a countable discrete space V, every nondegenerate separable
C*-correspondence over c_0(V) is isomorphic to one coming from a directed graph
with vertex set V. In this paper we demonstrate why the analogous
characterizations fail to hold for higher-rank graphs (where one considers
product systems of C*-correspondences) and for topological graphs (where V is
locally compact Hausdorff), and we discuss the obstructions that arise.Comment: major revision; stated some results in greater generalit
Making Photography Matter: A Viewer\u27s History from the Civil War to the Great Depression
Review of: "Making Photography Matter: A Viewer’s History from the Civil War to the Great Depression," by Cara A. Finnegan
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