Geodesic
The Exponential Map for Hopf Algebras
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an element of the Lie group. We give interpretations as states on the Hopf algebra, elements of a Hilbert $C^{*} $-bimodule of $\frac{1}{2}$ densities and elements of the dual Hopf algebra. We give examples for complex valued functions on the groups $S_{3}$ and $\mathbb{Z}$, Woronowicz's matrix quantum group $\mathbb{C}_{q}[SU_2] $ and the Sweedler–Taft algebra.
Keywords: Hopf algebra, differential calculus, Lie algebra, exponential map. 
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     author = {Ghaliah Alhamzi and Edwin Beggs},
     title = {The {Exponential} {Map} for {Hopf} {Algebras}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a16/}
}
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Ghaliah Alhamzi; Edwin Beggs. The Exponential Map for Hopf Algebras. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a16/

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