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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2014 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2014
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146623 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Groupoid Actions on Fractafolds / M. Ionescu, A. Kumjian // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-146623 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Groupoid Actions on Fractafolds |
| spellingShingle |
Groupoid Actions on Fractafolds Ionescu, M. Kumjian, A. |
| title_short |
Groupoid Actions on Fractafolds |
| title_full |
Groupoid Actions on Fractafolds |
| title_fullStr |
Groupoid Actions on Fractafolds |
| title_full_unstemmed |
Groupoid Actions on Fractafolds |
| title_sort |
groupoid actions on fractafolds |
| author |
Ionescu, M. Kumjian, A. |
| author_facet |
Ionescu, M. Kumjian, A. |
| publishDate |
2014 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/146623 |
| citation_txt |
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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AT ionescum groupoidactionsonfractafolds AT kumjiana groupoidactionsonfractafolds |
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2025-11-28T01:22:41Z |
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2025-11-28T01:22:41Z |
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1850853129607708672 |