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Journal of the London Mathematical Society Advance Access originally published online on January 17, 2007
Journal of the London Mathematical Society 2007 75(1):83-98; doi:10.1112/jlms/jdl007
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© 2007 London Mathematical Society

Co-representation theory of universal co-sovereign Hopf algebras

Julien Bichon

Laboratoire de Mathématiques Appliquées
Université de Pau et des Pays de l’Adour
IPRA
Avenue de l’université
64000 Pau
France
julien.bichon{at}univ-pau.fr

We determine the co-representation theory of the universal co-sovereign Hopf algebras, which are some natural analogues of the general linear groups in quantum group theory, for generic matrices over an algebraically closed field of characteristic zero. Our results generalize Banica's previous results in the compact case. As an application, we easily get the representation theory of the quantum automorphism group of a matrix algebra endowed with a non-necessarily tracial measure.

2000 Mathematics Subject Classification 16W30.

revised October 17, 2005; published online January 17, 2007.


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