A note on the antipode for algebraic quantum groups. (Q2888778)
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scientific article; zbMATH DE number 6042597
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the antipode for algebraic quantum groups. |
scientific article; zbMATH DE number 6042597 |
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4 June 2012
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multiplier Hopf algebras
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integrals
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algebraic quantum groups
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antipodes
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grouplike elements
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0.8967161
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0.8938294
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0.8930334
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A note on the antipode for algebraic quantum groups. (English)
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\textit{D. E. Radford} [Am. J. Math. 98, 333-355 (1976; Zbl 0332.16007)] proved a formula for the fourth power of the antipode of a finite dimensional Hopf algebra \(H\) in terms of the inner actions determined by the distinguished grouplike elements of \(H\) and its dual \(H^*\) on \(H\). \textit{M. Beattie, D. Bulacu} and \textit{B. Torrecillas} [J. Algebra 307, No. 1, 330-342 (2007; Zbl 1115.16016)] extended this formula to the case where \(H\) is a Hopf algebra with non-zero integrals. -- In the paper under review, the formula is extended even more, to the case of regular multiplier Hopf algebras with integrals.
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