Title: The Drinfel'd double versus the Heisenberg double for an algebraic quantum group
Authors: Delvaux, L ×
Van Daele, Alphons #
Issue Date: 2004
Publisher: Elsevier science bv
Series Title: Journal of Pure and Applied Algebra vol:190 issue:1-3 pages: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.
ISSN: 0022-4049
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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