A Diagrammatic Temperley-Lieb Categorification
The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/530808 |
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| author | Ben Elias |
| author_facet | Ben Elias |
| author_sort | Ben Elias |
| collection | DOAJ |
| description | The monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also
given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra. |
| format | Article |
| id | doaj-art-1154e2a9582f49148d8fc4e2ed51ea22 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1154e2a9582f49148d8fc4e2ed51ea222025-08-20T02:01:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/530808530808A Diagrammatic Temperley-Lieb CategorificationBen Elias0Department of Mathematics, Columbia University, New York, NY 10027, USAThe monoidal category of Soergel bimodules categorifies the Hecke algebra of a finite Weyl group. In the case of the symmetric group, morphisms in this category can be drawn as graphs in the plane. We define a quotient category, also given in terms of planar graphs, which categorifies the Temperley-Lieb algebra. Certain ideals appearing in this quotient are related both to the 1-skeleton of the Coxeter complex and to the topology of 2D cobordisms. We demonstrate how further subquotients of this category will categorify the irreducible modules of the Temperley-Lieb algebra.http://dx.doi.org/10.1155/2010/530808 |
| spellingShingle | Ben Elias A Diagrammatic Temperley-Lieb Categorification International Journal of Mathematics and Mathematical Sciences |
| title | A Diagrammatic Temperley-Lieb Categorification |
| title_full | A Diagrammatic Temperley-Lieb Categorification |
| title_fullStr | A Diagrammatic Temperley-Lieb Categorification |
| title_full_unstemmed | A Diagrammatic Temperley-Lieb Categorification |
| title_short | A Diagrammatic Temperley-Lieb Categorification |
| title_sort | diagrammatic temperley lieb categorification |
| url | http://dx.doi.org/10.1155/2010/530808 |
| work_keys_str_mv | AT benelias adiagrammatictemperleyliebcategorification AT benelias diagrammatictemperleyliebcategorification |