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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
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.
URI: http://hdl.handle.net/1942/13139
DOI: 10.4153/CMB-2011-079-4
ISI #: 000304726300005
ISSN: 0008-4395
Category: A1
Type: Journal Contribution
Validation: ecoom, 2013
Appears in Collections: Research publications

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