Please use this identifier to cite or link to this item:
Title: The Drinfel'd double versus the Heisenberg double for an algebraic quantum group
Authors: DELVAUX, Lydia 
Van Daele, A
Issue Date: 2004
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,
Document URI:
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

Show full item record


checked on Sep 5, 2020


checked on May 13, 2022

Page view(s)

checked on May 16, 2022

Google ScholarTM



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