Search for a basis of the Temperley-Lieb algebra, using rewriting systems
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the Temperley-Lieb algebra, which is an oriented version of the previous one. This pushes us to employ a more efficient tool, category theory, to use rewriting to easily obtain a basis for the algebra.
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