representation theory categorification 2 representation theory monoids monoidal categories mathematics algebras history quantum topology planar algebras gröbner bases discrete fourier transform fast fourier transform fast multiplication computer algebra geometry jones polynomial topology quantum algebra knot invariants knot theory classification theorems green's relations adjunctions 2-categories categorifcation algebra category theory knots categorical representations low-dimensional topology ade classifications subfactors vertex models history of mathematics diagrammatic algebra quantum groups
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