Abstract:

TThe Temperley--Lieb algebra (TL) is a classical mathematical object studied in algebra, combinatorics, statistical mechanics and mathematical physics, introduced by Temperley and Lieb in 1971. This algebra can be represented as a diagram algebra, i.e. an algebra having some planar diagrams as basis. More in general, it is possible to define the so-called generalized TL algebra for any Coxeter system. In this talk we will first introduce the Coxeter systems and a particular subset of "fully commutative elements". Then we will define the diagrams that form the basis of the classical TL algebra. Finally we will extend the definition of TL algebra and introduce diagrammatic representations for some of the affine (infinite) types.