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A Diagrammatic Temperley-Lieb Categorification.
- Source :
-
International Journal of Mathematics & Mathematical Sciences . 2010, p1-47. 47p. 76 Diagrams. - Publication Year :
- 2010
-
Abstract
- 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 irreduciblemodules of the Temperley-Lieb algebra. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01611712
- Database :
- Academic Search Index
- Journal :
- International Journal of Mathematics & Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 56504321
- Full Text :
- https://doi.org/10.1155/2010/530808