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Groupoid Actions on Fractafolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2014, том 10
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Groupoid Actions on Fractafolds
Інший ID:
2010 Mathematics Subject Classification: 28A80; 22A22; 46L55; 46L05
DOI:10.3842/SIGMA.2014.068
DOI:10.3842/SIGMA.2014.068
Посилання:
Groupoid Actions on Fractafolds / M. Ionescu, A. Kumjian // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
The work of the first author was partially supported by a grant from the Simons Foundation
(#209277 to Marius Ionescu). The authors would like to thank the referees for their helpful
comments.
Дата:
2014
Переглядів:
422
Завантажень:
231
Анотація:
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 C∗-algebra is primitive and has a densely defined lower-semicontinuous trace.
