Representation rings for fusion systems and dimension functions
We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a list of conditions for...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2018
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| Online Access: | http://hdl.handle.net/1721.1/114302 https://orcid.org/0000-0002-4913-8268 |
| _version_ | 1811095920444440576 |
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| author | Yalçın, Ergün Reeh, Sune Nikolaj Precht |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Yalçın, Ergün Reeh, Sune Nikolaj Precht |
| author_sort | Yalçın, Ergün |
| collection | MIT |
| description | We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a list of conditions for an F-stable super class function to be realized as the dimension function of an F-stable virtual representation. We also give an application of our results to constructions of finite group actions on homotopy spheres. |
| first_indexed | 2024-09-23T16:34:10Z |
| format | Article |
| id | mit-1721.1/114302 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:34:10Z |
| publishDate | 2018 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1143022022-09-29T20:09:40Z Representation rings for fusion systems and dimension functions Yalçın, Ergün Reeh, Sune Nikolaj Precht Massachusetts Institute of Technology. Department of Mathematics Reeh, Sune Nikolaj Precht We define the representation ring of a saturated fusion system F as the Grothendieck ring of the semiring of F-stable representations, and study the dimension functions of F-stable representations using the transfer map induced by the characteristic idempotent of F. We find a list of conditions for an F-stable super class function to be realized as the dimension function of an F-stable virtual representation. We also give an application of our results to constructions of finite group actions on homotopy spheres. Danish Council for Independent Research (DFF–4002-00224) 2018-03-27T13:35:53Z 2018-03-27T13:35:53Z 2017-05 2018-03-14T04:57:47Z Article http://purl.org/eprint/type/JournalArticle 0025-5874 1432-1823 http://hdl.handle.net/1721.1/114302 Reeh, Sune Precht, and Ergün Yalçın. “Representation Rings for Fusion Systems and Dimension Functions.” Mathematische Zeitschrift, vol. 288, no. 1–2, Feb. 2018, pp. 509–30. https://orcid.org/0000-0002-4913-8268 en http://dx.doi.org/10.1007/s00209-017-1898-8 Mathematische Zeitschrift Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Yalçın, Ergün Reeh, Sune Nikolaj Precht Representation rings for fusion systems and dimension functions |
| title | Representation rings for fusion systems and dimension functions |
| title_full | Representation rings for fusion systems and dimension functions |
| title_fullStr | Representation rings for fusion systems and dimension functions |
| title_full_unstemmed | Representation rings for fusion systems and dimension functions |
| title_short | Representation rings for fusion systems and dimension functions |
| title_sort | representation rings for fusion systems and dimension functions |
| url | http://hdl.handle.net/1721.1/114302 https://orcid.org/0000-0002-4913-8268 |
| work_keys_str_mv | AT yalcınergun representationringsforfusionsystemsanddimensionfunctions AT reehsunenikolajprecht representationringsforfusionsystemsanddimensionfunctions |