Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/13139
Title: A note on the antipode for algebraic quantum groups
Authors: DELVAUX, Lydia 
Van Daele, A.
Wang, S.
Issue Date: 2012
Source: CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 55, p. 260-270.
Abstract: Recently, Beattie, Bulacu ,and Torrecillas proved Radford's formula for the fourth power of the antipode for a co-Frobenius Hopf algebra. In this note, we show that this formula can be proved for any regular multiplier Hopf algebra with integrals (algebraic quantum groups). This, of course, not only includes the case of a finite-dimensional Hopf algebra, but also that of any Hopf algebra with integrals (co-Frobenius Hopf algebras). Moreover, it turns out that the proof in this more general situation, in fact, follows in a few lines from well-known formulas obtained earlier in the theory of regular multiplier Hopf algebras with integrals. We discuss these formulas and their importance in this theory. We also mention their generalizations, in particular to the (in a certain sense) more general theory of locally compact quantum groups. Doing so, and also because the proof of the main result itself is very short, the present note becomes largely of an expository nature.
Keywords: multiplier Hopf algebras; algebraic quantum groups; the antipode
Document URI: http://hdl.handle.net/1942/13139
ISSN: 0008-4395
e-ISSN: 1496-4287
DOI: 10.4153/CMB-2011-079-4
ISI #: 000304726300005
Category: A1
Type: Journal Contribution
Validations: ecoom 2013
Appears in Collections:Research publications

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