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The braid group appears in many scientific fields and its representations areinstrumental in understanding topological quantum algorithms, topologicalentropy, classification of manifolds and so on. In this work, we study planerdiagrams which are Kauffman's reduction of the braid group algebra to theTemperley-Lieb algebra. We introduce an algorithm for computing all planerdiagrams in a given dimension. The algorithm can also be used to multiplyplaner diagrams and find their matrix representation.

Algorithm for computing Representations of the Braid Group and Temperley-Lieb algebra