Finite quantum groups and quantum permutation groups
Copyright policy )Finite quantum groups and quantum permutation groups
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.
latex, 17 pages
Mathematics(all), semisimple Hopf algebra, Quantum groups (quantized enveloping algebras) and related deformations, bismash products, 16T05, 46L65, quantum permutation groups, Hopf algebra, Extension, Mathematics - Quantum Algebra, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Quantum Algebra (math.QA), https://purl.org/becyt/ford/1, exact factorizations of finite groups, Hopf algebras and their applications, Group rings, Bismash product, finite quantum groups, Quantum permutation group, Quantizations, deformations for selfadjoint operator algebras, Products of subgroups of abstract finite groups, finite-dimensional Hopf algebras, extensions, quantum permutation group
Mathematics(all), semisimple Hopf algebra, Quantum groups (quantized enveloping algebras) and related deformations, bismash products, 16T05, 46L65, quantum permutation groups, Hopf algebra, Extension, Mathematics - Quantum Algebra, FOS: Mathematics, https://purl.org/becyt/ford/1.1, Quantum Algebra (math.QA), https://purl.org/becyt/ford/1, exact factorizations of finite groups, Hopf algebras and their applications, Group rings, Bismash product, finite quantum groups, Quantum permutation group, Quantizations, deformations for selfadjoint operator algebras, Products of subgroups of abstract finite groups, finite-dimensional Hopf algebras, extensions, quantum permutation group
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