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Title: | The representation theory of non-commutative O(GL(2)) | Authors: | RAEDSCHELDERS, Theo VAN DEN BERGH, Michel |
Issue Date: | 2017 | Publisher: | EUROPEAN MATHEMATICAL SOC | Source: | 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. | Keywords: | Hopf algebras; monoidal categories; quasi-hereditary algebras;Hopf algebras; monoidal categories; quasi-hereditary algebras | Document URI: | http://hdl.handle.net/1942/26392 | ISSN: | 1661-6952 | e-ISSN: | 1661-6960 | DOI: | 10.4171/JNCG/11-3-3 | ISI #: | 000418004600003 | Rights: | © European Mathematical Society | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2019 |
Appears in Collections: | Research publications |
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raedschelders2017.pdf Restricted Access | Published version | 401.67 kB | Adobe PDF | View/Open Request a copy |
Vandenbergh.pdf | Non Peer-reviewed author version | 399.9 kB | Adobe PDF | View/Open |
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