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Quantum automorphism groups of small metric spaces
To any finite metric space we associate the universal Hopf \c^*-algebra
coacting on . We prove that spaces having at most 7 points fall into
one of the following classes: (1) the coaction of is not transitive; (2)
is the algebra of functions on the automorphism group of ; (3) is a
simplex and corresponds to a Temperley-Lieb algebra; (4) is a product
of simplexes and corresponds to a Fuss-Catalan algebra.Comment: 22 page
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