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• W2964271472 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 H+(p,0)≈QISO(Fpˆ), where the latter can be viewed as a liberation of the classical isometry group of the p-dimensional torus." @default.
• W2964271472 created "2019-07-30" @default.
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• W2964271472 date "2011-06-01" @default.
• W2964271472 modified "2023-09-26" @default.
• W2964271472 title "Two-parameter families of quantum symmetry groups" @default.
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• W2964271472 doi "https://doi.org/10.1016/j.jfa.2010.11.016" @default.
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