Quantum groups acting on 4 points

Teodor Banica; Julien Bichon

doi:10.1515/CRELLE.2009.003

Published by De Gruyter January 8, 2009

Quantum groups acting on 4 points

Teodor Banica and Julien Bichon

From the journal Journal für die reine und angewandte Mathematik

https://doi.org/10.1515/CRELLE.2009.003

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Abstract

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group 𝓠₄. Our main tool is a new presentation for the algebra C(𝓠₄), corresponding to an isomorphism of type 𝓠₄ ≃ SO_–1(3). The quantum subgroups of 𝓠₄ are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.

Received: 2007-05-24

Revised: 2007-09-04

Published Online: 2009-01-08

Published in Print: 2009-January

Quantum groups acting on 4 points

Abstract

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