Two-parameter families of quantum symmetry groups |
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Authors: | Teodor Banica |
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Affiliation: | a Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise, France b Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom c Mathematical Institute of the Polish Academy of Sciences, ul. ?niadeckich 8, 00-956 Warszawa, Poland |
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Abstract: | We introduce and study natural two-parameter families of quantum groups motivated on one hand by the liberations of classical orthogonal groups and on the other by quantum isometry groups of the duals of the free groups. Specifically, for each pair (p,q) of non-negative integers we define and investigate quantum groups O+(p,q), B+(p,q), S+(p,q) and H+(p,q) corresponding to, respectively, orthogonal groups, bistochastic groups, symmetric groups and hyperoctahedral groups. In the first three cases the new quantum groups turn out to be related to the (dual free products of ) free quantum groups studied earlier. For H+(p,q) the situation is different and we show that , where the latter can be viewed as a liberation of the classical isometry group of the p-dimensional torus. |
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Keywords: | Quantum symmetry groups Quantum isometry groups Liberation Representation theory of quantum groups Tannakian categories |
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