Journal of Noncommutative Geometry

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Volume 8, Issue 1, 2014, pp. 107–140
DOI: 10.4171/JNCG/150

Published online: 2014-03-20

Quantum groups of GL(2) representation type

Colin Mrozinski[1]

(1) Université Blaise Pascal, Aubière, France

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.

Keywords: Quantum groups, Hopf algebra, monoidal category, cogroupoid

Mrozinski Colin: Quantum groups of GL(2) representation type. J. Noncommut. Geom. 8 (2014), 107-140. doi: 10.4171/JNCG/150