In our companion paper "The Manin Hopf algebra of a Koszul Artin–Schelter regular algebra is quasi-hereditary" we used the Tannaka–Krein formalism to study the universal coacting Hopf algebra for a Koszul Artin–Schelter regular algebra . In this paper we study in detail the case . In particular we give a more precise description of the standard and costandard representations of as a coalgebra and we show that the latter can be obtained by induction from a Borel quotient algebra. Finally we give a combinatorial characterization of the simple -representations as tensor products of -representations and their duals.
Cite this article
Theo Raedschelders, Michel Van den Bergh, The representation theory of non-commutative (GL. J. Noncommut. Geom. 11 (2017), no. 3, pp. 845–885DOI 10.4171/JNCG/11-3-3