an:06042597
Zbl 1252.16028
Delvaux, L.; Van Daele, A.; Wang, Shuanhong
A note on the antipode for algebraic quantum groups
EN
Can. Math. Bull. 55, No. 2, 260-270 (2012).
00300368
2012
j
16T05 16T20 17B37 46L65
multiplier Hopf algebras; integrals; algebraic quantum groups; antipodes; grouplike elements
\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.
Sorin Dascalescu (Bucure??ti)
Zbl 0332.16007; Zbl 1115.16016