Journal of the Ramanujan Mathematical Society

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The Hyperoctahedral Quantum Group


Affiliations
1 Department of Mathematics, Paul Sabatier University, 118 Route de Narbonne, 31062 Toulouse, France
2 Department of Mathematics, Blaise Pascal University, Campus des Cezeaux, 63177 Aubiere Cedex, France
3 Department of Mathematics, Claude Bernard University, 43 bd du 11 November 1918, 69622 Villeurbanne, France
     

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We consider the hypercube in Rn, and show that its quantum symmetry group is a q-deformation of On at q = −1. Then we consider the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted H+n , enlarges Wang’s series S+n , O+n , U+n.
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  • The Hyperoctahedral Quantum Group

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Authors

Teodor Banica
Department of Mathematics, Paul Sabatier University, 118 Route de Narbonne, 31062 Toulouse, France
Julien Bichon
Department of Mathematics, Blaise Pascal University, Campus des Cezeaux, 63177 Aubiere Cedex, France
Benoit Collins
Department of Mathematics, Claude Bernard University, 43 bd du 11 November 1918, 69622 Villeurbanne, France

Abstract


We consider the hypercube in Rn, and show that its quantum symmetry group is a q-deformation of On at q = −1. Then we consider the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted H+n , enlarges Wang’s series S+n , O+n , U+n.