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- W4367190624 abstract "Let $(A,Delta)$ be a finite-dimensional Hopf algebra. The linear dual $B$ of $A$ is again a finite-dimensional Hopf algebra. The duality is given by an element $Vin Botimes A$, defined by $langle V,aotimes brangle=langle a,brangle$ where $ain A$ and $bin B$. We use $langle,cdot, , ,cdot,rangle$ for the pairings. In the introduction of this paper, we recall the various properties of this element $V$ as sitting in the algebra $Botimes A$. More generally, we can consider an algebraic quantum group $(A,Delta)$. We use the term here for a regular multiplier Hopf algebra with integrals. For $B$ we now take the dual $widehat A$ of $A$. It is again an algebraic quantum group. In this case, the duality gives rise to an element $V$ in the multiplier algebra $M(Botimes A)$. Still, most of the properties of $V$ in the finite-dimensional case are true in this more general setting. The focus in this paper lies on various aspects of the duality between $A$ and its dual $widehat A$. Among other things we include a number of formulas relating the objects associated with an algebraic quantum group and its dual. This note is meant to give a comprehensive, yet concise (and sometimes simpler) account of these known results. This is part I of a series of three papers on this subject. The case of a multiplier Hopf $^*$-algebra with positive integrals is treated in detail in part II and part III." @default.
- W4367190624 created "2023-04-28" @default.
- W4367190624 creator A5027202272 @default.
- W4367190624 date "2023-04-26" @default.
- W4367190624 modified "2023-09-25" @default.
- W4367190624 title "Algebraic quantum groups and duality I" @default.
- W4367190624 doi "https://doi.org/10.48550/arxiv.2304.13448" @default.
- W4367190624 hasPublicationYear "2023" @default.
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