Quantum groups acting on 4 points

Details Quantum groups acting on 4 points Quantum groups acting on 4 points

2007-03-05

arxiv.org/abs/math/0703118v2

J. Reine Angew. Math. 626 (2009), 74-114

Mathematics

Quantum Algebra

34 pages. Comments added in last section

Scientific paper

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group $\mathcal Q_4$. Our main tool is a new presentation for the algebra $\rm C(\mathcal Q_4)$, corresponding to an isomorphism of type $\mathcal Q_4\simeq SO_{-1}(3)$. The quantum subgroups of $\mathcal Q_4$ are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.

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