English

Groupoid Actions on Fractafolds

Dynamical Systems 2014-07-01 v2 Functional Analysis Operator Algebras

Abstract

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 CC^*-algebra is primitive and has a densely defined lower-semicontinuous trace.

Keywords

Cite

@article{arxiv.1311.3880,
  title  = {Groupoid Actions on Fractafolds},
  author = {Marius Ionescu and Alex Kumjian},
  journal= {arXiv preprint arXiv:1311.3880},
  year   = {2014}
}

Comments

SIGMA 10 (2014), 068, 14 pages

R2 v1 2026-06-22T02:08:22.323Z