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 w...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146623 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Groupoid Actions on Fractafolds / M. Ionescu, A. Kumjian // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862601091397451776 |
|---|---|
| author | Ionescu, M. Kumjian, A. |
| author_facet | Ionescu, M. Kumjian, A. |
| citation_txt | Groupoid Actions on Fractafolds / M. Ionescu, A. Kumjian // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-28T01:22:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146623 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-28T01:22:41Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ionescu, M. Kumjian, A. 2019-02-10T10:14:53Z 2019-02-10T10:14:53Z 2014 Groupoid Actions on Fractafolds / M. Ionescu, A. Kumjian // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 28A80; 22A22; 46L55; 46L05 DOI:10.3842/SIGMA.2014.068 https://nasplib.isofts.kiev.ua/handle/123456789/146623 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Groupoid Actions on Fractafolds Article published earlier |
| spellingShingle | Groupoid Actions on Fractafolds Ionescu, M. Kumjian, A. |
| title | Groupoid Actions on Fractafolds |
| title_full | Groupoid Actions on Fractafolds |
| title_fullStr | Groupoid Actions on Fractafolds |
| title_full_unstemmed | Groupoid Actions on Fractafolds |
| title_short | Groupoid Actions on Fractafolds |
| title_sort | groupoid actions on fractafolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146623 |
| work_keys_str_mv | AT ionescum groupoidactionsonfractafolds AT kumjiana groupoidactionsonfractafolds |