Quantum automorphism groups of small metric spaces

Original · EN

To any finite metric space X we associate the universal Hopf -algebra H coacting on X. We prove that spaces X having at most 7 points fall into one of the following classes: (1) the coaction of H is not transitive; (2) H is the algebra of functions on the automorphism group of X; (3) X is a simplex and H corresponds to a Temperley-Lieb algebra; (4) X is a product of simplexes and H corresponds to a Fuss-Catalan algebra.