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http://hdl.handle.net/1942/2187
Title: | The Drinfel'd double versus the Heisenberg double for an algebraic quantum group | Authors: | DELVAUX, Lydia Van Daele, A |
Issue Date: | 2004 | Publisher: | ELSEVIER SCIENCE BV | Source: | JOURNAL OF PURE AND APPLIED ALGEBRA, 190(1-3). p. 59-84 | Abstract: | Let A be a regular multiplier Hopf algebra with integrals. The dual of A, denoted by (A) over cap, is a multiplier Hopf algebra so that <(A) over cap ,A> is a pairing of multiplier Hopf algebras. We consider the Drinfel'd double, D = (A) over cap A(cop), associated to this pair. We prove that D is a quasitriangular multiplier Hopf algebra. More precisely, we show that the pair <(A) over cap ,A> has a "canonical multiplier" W epsilon M((A) over cap circle times A). The image of W in M(D circle times D) is a generalized R-matrix for D. We use this image of W to deform the product of the dual multiplier Hopf algebra D via the right action of D on (D) over cap which defines the pair <(D) over cap ,D>. As expected from the finite-dimensional case, we find that the deformation of the product in (D) over cap is related to the Heisenberg double A#(A) over cap. (C) 2003 Elsevier B.V. All rights reserved. | Notes: | Limburgs Univ Ctr, Dept Math, B-3590 Diepenbeek, Belgium. Katholieke Univ Leuven, Dept Math, B-3001 Heverlee, Belgium.Delvaux, L, Limburgs Univ Ctr, Dept Math, Universiteitslaan, B-3590 Diepenbeek, Belgium.lydia.delvaux@luc.ac.be alfons.vandaele@wis.kuleuven.ac.be | Document URI: | http://hdl.handle.net/1942/2187 | ISSN: | 0022-4049 | e-ISSN: | 1873-1376 | DOI: | 10.1016/j.jpaa.2003.10.031 | ISI #: | 000220643800005 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2005 |
Appears in Collections: | Research publications |
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