Eva C. Farkas
Hopf algebras of smooth functions on compact Lie groups

Comment.Math.Univ.Carolinae 41,4 (2000) 651-661.

Abstract: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.

Keywords: $C^{\infty }$-Hopf-algebras, algebras of smooth functions on compact Lie groups, duality theorem
AMS Subject Classification: 16W30, 22D35, 22E15, 46E25

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