Quantum groups of GL(2) representation type

Colin Mrozinski (1)

1 Géométrie, Algèbre, Algèbre d'operateurs

We classify the cosemisimple Hopf algebras whose corepresentation semi-ring is isomorphic to that of GL(2). This leads us to define a new family of Hopf algebras which generalize the quantum similitude group of a non-degenerate bilinear form. A detailed study of these Hopf algebras gives us an isomorphic classification and the description of their corepresentation categories.

Mots clés: Hopf algebra; Monoidal category; Cogroupoid

Domaines: Algèbres quantiques [math.QA]; Anneaux et algèbres [math.RA]

Colin Mrozinski. Quantum groups of GL(2) representation type. 2012. ⟨hal-00660411⟩