Topological Defects in Lattice Models and Affine Temperley–Lieb Algebra

This paper is the first in a series where we attempt to define defects critical lattice models that give rise conformal field theory topological continuum limit. We focus mostly on based Temperley-Lieb algebra, with future applications restricted solid-on-solid (also called anyonic chains) models, as well non-unitary like percolation or self-avoiding walks. Our approach essentially algebraic and focusses from two points of view: "crossed channel" defect seen an operator acting Hilbert space "direct it corresponds modification basic Hamiltonian some sort impurity. Algebraic characterizations constructions are proposed both view. In crossed channel, this leads us new results about center affine algebra; particular find there special basis non-negative integer structure constants interpreted fusion rules defects. direct meanwhile, introduction products quotients, interesting properties allow describe representations content model defect, its spectrum.