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Title: | The Manin Hopf algebra of a Koszul Artin-Schelter regular algebra is quasi-hereditary | Authors: | RAEDSCHELDERS, Theo VAN DEN BERGH, Michel |
Issue Date: | 2017 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | ADVANCES IN MATHEMATICS, 305, p. 601-660 | Abstract: | For any Koszul Artin-Schelter regular algebra A, we consider the universal Hopf algebra (aut) under bar (A) coacting on A, introduced by Manin. To study the representations (i.e. finite dimensional comodules) of this Hopf algebra, we use the Tannaka-Krein formalism. Specifically, we construct an explicit combinatorial rigid monoidal category U, equipped with a functor M to finite dimensional vector spaces such that (aut) under bar (A) = coendu(M). Using this pair (U, M) we show that (aut) under bar (A) is quasi-hereditary as a coalgebra and in addition is derived equivalent to the representation category of U. (C) 2016 Elsevier Inc. All rights reserved. | Notes: | [Raedschelders, Theo] Vrije Univ Brussel, Dept Wiskunde, Pleinlaan 2, B-1050 Brussels, 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/1942/24357 | ISSN: | 0001-8708 | e-ISSN: | 1090-2082 | DOI: | 10.1016/j.aim.2016.09.017 | ISI #: | 000406169200014 | Rights: | © 2016 Elsevier Inc. All rights reserved. | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2018 |
Appears in Collections: | Research publications |
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