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Keywords:
$C^{\infty}$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem
$C^{\infty}$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem
Summary:
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.
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