Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11456
Title: Algebraic quantum hypergroups
Authors: DELVAUX, Lydia 
Van Daele, A.
Issue Date: 2011
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: ADVANCES IN MATHEMATICS, 226 (2). p. 1134-1167
Abstract: An algebraic quantum group is a regular multiplier Hopf algebra with integrals. In this paper we will develop a theory of algebraic quantum hypergroups. It is very similar to the theory of algebraic quantum groups, except that the comultiplication is no longer assumed to be a homomorphism. We still require the existence of a left and of a right integral. There is also an antipode but it is characterized in terms of these integrals. We construct the dual, just as in the case of algebraic quantum groups and we show that the dual of the dual is the original quantum hypergroup. We define algebraic quantum hypergroups of compact type and discrete type and we show that these types are dual to each other. The algebraic quantum hypergroups of compact type are essentially the algebraic ingredients of the compact quantum hypergroups as introduced and studied (in an operator algebraic context) by Chapovsky and Vainerman. We will give some basic examples in order to illustrate different aspects of the theory. In a separate note, we will consider more special cases and more complicated examples. In particular, in that note, we will give a general construction procedure and show how known examples of these algebraic quantum hypergroups fit into this framework. (C) 2010 Elsevier Inc. All rights reserved.
Notes: [Van Daele, A.] Katholieke Univ Leuven, Dept Math, B-3001 Heverlee, Belgium. [Delvaux, L.] Univ Hasselt, Dept Math, B-3590 Diepenbeek, Belgium. Alfons.VanDaele@wis.kuleuven.be
Keywords: Hopf algebras; Multiplier Hopf algebras; Algebraic quantum groups; Hypergroups
Document URI: http://hdl.handle.net/1942/11456
ISSN: 0001-8708
e-ISSN: 1090-2082
DOI: 10.1016/j.aim.2010.07.015
ISI #: 000284452900003
Category: A1
Type: Journal Contribution
Validations: ecoom 2011
Appears in Collections:Research publications

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