61 research outputs found
Groupoid Actions on Fractafolds
We define a bundle over a totally disconnected set such that each fiber is
homeomorphic to a fractal blowup. We prove that there is a natural action of a
Renault-Deaconu groupoid on our fractafold bundle and that the resulting action
groupoid is a Renault-Deaconu groupoid itself. We also show that when the
bundle is locally compact the associated -algebra is primitive and has a
densely defined lower-semicontinuous trace.Comment: SIGMA 10 (2014), 068, 14 page
Generalised morphisms of k-graphs: k-morphs
In a number of recent papers, (k+l)-graphs have been constructed from
k-graphs by inserting new edges in the last l dimensions. These constructions
have been motivated by C*-algebraic considerations, so they have not been
treated systematically at the level of higher-rank graphs themselves. Here we
introduce k-morphs, which provide a systematic unifying framework for these
various constructions. We think of k-morphs as the analogue, at the level of
k-graphs, of C*-correspondences between C*-algebras. To make this analogy
explicit, we introduce a category whose objects are k-graphs and whose
morphisms are isomorphism classes of k-morphs. We show how to extend the
assignment \Lambda \mapsto C*(\Lambda) to a functor from this category to the
category whose objects are C*-algebras and whose morphisms are isomorphism
classes of C*-correspondences.Comment: 27 pages, four pictures drawn with Tikz. Version 2: title changed and
numerous minor corrections and improvements. This version to appear in Trans.
Amer. Math. So
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