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The representation theory of non-commutative O(GL2)

Journal Contribution - Journal Article

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 aut(A) for a Koszul Artin–Schelter regular algebra A. In this paper we study in detail the case A=k[x,y]. In particular we give a more precise description of the standard and costandard representations of aut(A) 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 aut(A)-representations as tensor products of end(A)-representations and their duals.
Journal: Journal of Noncommutative Geometry
ISSN: 1661-6952
Issue: 3
Volume: 11
Pages: 845-885
Number of pages: 41
Publication year:2017