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HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS

Published online by Cambridge University Press:  25 August 2010

TEODOR BANICA  and
JULIEN BICHON
TEODOR BANICA
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, 2 avenue Chauvin, 95302 Cergy-Pontoise, France e-mail: Teodor.Banica@u-cergy.fr
JULIEN BICHON
Affiliation:
Laboratoire de Mathématiques, Université Blaise Pascal, Clermont-Ferrand II, Campus des Cézeaux, 63177 Aubière Cedex, France e-mail: Julien.Bichon@math.univ-bpclermont.fr
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Abstract

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We develop a general theory of Hopf image of a Hopf algebra representation, with the associated concept of inner faithful representation, modelled on the notion of faithful representation of a discrete group. We study several examples, including group algebras, enveloping algebras of Lie algebras, pointed Hopf algebras, function algebras, twistings and cotwistings, and we present a Tannaka duality formulation of the notion of Hopf image.

Keywords

16W30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 677 - 703
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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