Quantum groups acting on 4 points

Abstract

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group ∂ 4. Our main tool is a new presentation for the algebra C(∂ 4), corresponding to an isomorphism of type ∂ 4 ≃ SO -1(3). The quantum subgroups of ∂ 4 are subject to a McKay type correspondence, that we describe at the level of algebraic invariants. © 2009 Walter de Gruyter.