HOPF IMAGES AND INNER FAITHFUL REPRESENTATIONS
By T. Banica, Julien Bichon. Glasgow Mathematical Journal, 2008
60 citations recorded by the source corpus.
Abstract 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.
View Paper: https://www.semanticscholar.org/paper/15ce7ee2100f8d172994e1cd76903adc06eb557a
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- Michael Brannan
- Benoît Collins
- Roland Vergnioux
- Chelsea M. Walton
- Pavel Etingof
- T. Banica
- Roland Speicher
- I. Gordon
Citations in the corpus
- Semisimple Hopf actions on commutative domains (2013, background): “ht) if Ais a right K-comodule and ρ(ab) = ρ(a)ρ(b) for all a,b∈ A. We also want to restrict ourselves to H-actions (and K-coactions) that do not factor through ‘smaller’ Hopf algebras. Definition 2.2. [BB10] Given a left H-module M, we say that Mis inner faithful over H, if IM6= 0 for every nonzero H”
- The Connes embedding property for quantum group von Neumann algebras (2014, background): “[4], andα is inner faithful iff its Hopf image is(G, ι).”