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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/26392

Title: The representation theory of non-commutative O(GL(2))
Authors: Raedschelders, Theo
Van den Bergh, Michel
Issue Date: 2017
Publisher: EUROPEAN MATHEMATICAL SOC
Citation: JOURNAL OF NONCOMMUTATIVE GEOMETRY, 11(3), p. 845-885
Abstract: 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)under bar(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)under bar(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)under bar(A)-representations as tensor products of (end)under bar(A)-representations and their duals.
Notes: [Raedschelders, Theo; Van den Bergh, Michel] FWO, Brussels, Belgium. [Raedschelders, Theo] Vrije Univ Brussel, Dept Wiskunde, Pl Laan 2, B-1050 Elsene, Belgium. [Van den Bergh, Michel] Univ Hasselt, Dept WNI, Univ Campus, B-3590 Diepenbeek, Belgium.
URI: http://hdl.handle.net/1942/26392
DOI: 10.4171/JNCG/11-3-3
ISI #: 000418004600003
ISSN: 1661-6952
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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