Quantum automorphism groups of small metric spaces

Teodor Banica

Vol. 219 (2005), No. 1, 27–51

DOI: 10.2140/pjm.2005.219.27

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 2000

Primary: 16W30

Secondary: 46L37, 81R50

Milestones

Received: 30 April 2003

Revised: 10 February 2004

Published: 1 March 2005