280 research outputs found
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-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 cell
modules of the Temperley-Lieb algebra.Comment: long awaited update to published versio
The center of the affine nilTemperley-Lieb algebra
We give a description of the center of the affine nilTemperley-Lieb algebra
based on a certain grading of the algebra and on a faithful representation of
it on fermionic particle configurations. We present a normal form for
monomials, hence construct a basis of the algebra, and use this basis to show
that the affine nilTemperley-Lieb algebra is finitely generated over its
center. As an application, we obtain a natural embedding of the affine
nilTemperley-Lieb algebra on N generators into the affine nilTemperley-Lieb
algebra on N + 1 generators.Comment: 27 pages, 5 figures, comments welcom
An alternative basis for the Kauffman bracket skein module of the Solid Torus via braids
In this paper we give an alternative basis, , for the
Kauffman bracket skein module of the solid torus, . The basis is obtained with the use of the
Tempereley--Lieb algebra of type B and it is appropriate for computing the
Kauffman bracket skein module of the lens spaces via braids.Comment: 14 pages, 5 figure
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