Finite quantum groups and quantum permutation groups

TEODOR BANICA, JULIEN BICHON Y SONIA NATALE

ADVANCES IN MATHEMATICS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2012 vol. 229 p. 3320 - 3338

0001-8708

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 S_4 = Z_4 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.