Finite quantum groups and quantum permutation groups

Details Finite quantum groups and quantum permutation groups Finite quantum groups and quantum permutation groups

2011-04-07

arxiv.org/abs/1104.1400v1

Adv. Math. 229 (2012), 3320-3338

Mathematics

Quantum Algebra

latex, 17 pages

Scientific paper

We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not quantum permutation groups: one such example occurs as a split abelian extension associated to the exact factorization $\mathbb S_4 = \mathbb Z_4 \mathbb S_3$ and has dimension 24. We show that, in fact, this is the smallest possible dimension that a non quantum permutation group can have.

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