147 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
Irreducible Induced Representations of Fell Bundle C*-Algebras
We give precise conditions under which irreducible representations associated
to stability groups induce to irreducible representations for Fell bundle
C*-algebras. This result generalizes an earlier result of Echterhoff and the
second author. Because the Fell bundle construction subsumes most other
examples of C*-algebras constructed from dynamical systems, our result
percolates down to many different constructions including the many flavors of
groupoid crossed products.Comment: Minor changes suggested by the referee. The paper is accepted for
publication in Trans. Amer. Math. So
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