Quantum groups acting on 4 points : Journal für die reine und angewandte Mathematik (Crelles Journal)

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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk


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Quantum groups acting on 4 points

Teodor Banica1 / Julien Bichon2

1Laboratoire de Mathématiques, Université Paul Sabatier, Toulouse III, 118 route de Narbonne, 31062 Toulouse, France. e-mail:

2Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand II, Campus des Cézeaux, 63177 Aubière Cedex, France. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 626, Pages 75–114, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.003, January 2009

Publication History

Received:
2007-05-24
Revised:
2007-09-04
Published Online:
2009-01-08

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 𝓠4SO –1(3). The quantum subgroups of 𝓠4 are subject to a McKay type correspondence, that we describe at the level of algebraic invariants.

Citing Articles

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[1]
Teodor Banica and Julien Bichon
International Mathematics Research Notices, 2015, Volume 2015, Number 24, Page 13406
[2]
TEODOR BANICA and JULIEN BICHON
Glasgow Mathematical Journal, 2010, Volume 52, Number 03, Page 677
[3]
Colin Mrozinski
Journal of Pure and Applied Algebra, 2015, Volume 219, Number 1, Page 1
[4]
Matthew Daws, Paweł Kasprzak, Adam Skalski, and Piotr M. Sołtan
Advances in Mathematics, 2012, Volume 231, Number 6, Page 3473
[5]
Julien Bichon and Sonia Natale
Transformation Groups, 2011, Volume 16, Number 2, Page 339

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