Constructing the extended Haagerup planar algebra
We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range (4,3+√3), which was initiated by Haagerup in 1993. We prove that the subfac...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2016
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| Online Access: | http://hdl.handle.net/1721.1/105134 |
| _version_ | 1826190984952676352 |
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| author | Bigelow, Stephen Peters, Emily Morrison, Scott Snyder, Noah |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bigelow, Stephen Peters, Emily Morrison, Scott Snyder, Noah |
| author_sort | Bigelow, Stephen |
| collection | MIT |
| description | We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range (4,3+√3), which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein-theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein-theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram. This is the published version of arXiv:0909.4099 [math.OA]. |
| first_indexed | 2024-09-23T08:48:19Z |
| format | Article |
| id | mit-1721.1/105134 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:48:19Z |
| publishDate | 2016 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1051342022-09-23T14:41:16Z Constructing the extended Haagerup planar algebra Bigelow, Stephen Peters, Emily Morrison, Scott Snyder, Noah Massachusetts Institute of Technology. Department of Mathematics Peters, Emily We construct a new subfactor planar algebra, and as a corollary a new subfactor, with the ‘extended Haagerup’ principal graph pair. This completes the classification of irreducible amenable subfactors with index in the range (4,3+√3), which was initiated by Haagerup in 1993. We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein-theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. In the skein-theoretic description there is an explicit algorithm for evaluating closed diagrams. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram. This is the published version of arXiv:0909.4099 [math.OA]. National Science Foundation (U.S.) (Grant DMS-0401734) Soroptimist International (Fellowship) 2016-10-28T16:45:50Z 2016-10-28T16:45:50Z 2012-09 2010-01 2016-08-18T15:20:40Z Article http://purl.org/eprint/type/JournalArticle 0001-5962 1871-2509 http://hdl.handle.net/1721.1/105134 Bigelow, Stephen et al. “Constructing the Extended Haagerup Planar Algebra.” Acta Mathematica 209.1 (2012): 29–82. en http://dx.doi.org/10.1007/s11511-012-0081-7 Acta Mathematica 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. Institut Mittag-Leffler application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Bigelow, Stephen Peters, Emily Morrison, Scott Snyder, Noah Constructing the extended Haagerup planar algebra |
| title | Constructing the extended Haagerup planar algebra |
| title_full | Constructing the extended Haagerup planar algebra |
| title_fullStr | Constructing the extended Haagerup planar algebra |
| title_full_unstemmed | Constructing the extended Haagerup planar algebra |
| title_short | Constructing the extended Haagerup planar algebra |
| title_sort | constructing the extended haagerup planar algebra |
| url | http://hdl.handle.net/1721.1/105134 |
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