Journal of Noncommutative Geometry
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Published online: 2014-03-20
Quantum groups of GL(2) representation typeColin Mrozinski (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