Document Server@UHasselt >
Research >
Research publications >

Please use this identifier to cite or link to this item: 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
Citation: 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
URI: http://hdl.handle.net/1942/2187
DOI: 10.1016/j.jpaa.2003.10.031
ISI #: 000220643800005
ISSN: 0022-4049
Category: A1
Type: Journal Contribution
Validation: ecoom, 2005
Appears in Collections: Research publications

Files in This Item:

There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.