Geodesic
Hopf algebras of smooth functions on compact Lie groups
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 651-661.

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A $C^{\infty}$-Hopf algebra is a $C^{\infty}$-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those $C^{\infty}$-Hopf algebras which are given by the algebra $C^{\infty}(G)$ of smooth functions on some compact Lie group $G$, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.
Classification : 16W30, 22D35, 22E15, 46E25, 46J15
Keywords: $C^{\infty}$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem 
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     author = {Farkas, Eva C.},
     title = {Hopf algebras of smooth functions on compact {Lie} groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {651--661},
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     number = {4},
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Farkas, Eva C. Hopf algebras of smooth functions on compact Lie groups. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 651-661. http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a0/