Abstract

To any finite metric space X we associate the universal Hopf C^*-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 simplices and H corresponds to a Fuss–Catalan algebra.

Mathematical Subject Classification

Primary: 16W30

Secondary: 46L37, 81R50

Authors