Farkas, Eva C. Hopf algebras of smooth functions on compact Lie groups. (English) Zbl 1051.16021 Commentat. Math. Univ. Carol. 41, No. 4, 651-661 (2000). Let \(G\) be a Lie group and let \(C^\infty(G)\) be the algebra of smooth functions on \(G\). A \(C^\infty\)-algebra, which, at the same time, satisfies the axioms of a convenient Hopf algebra, is called a \(C^\infty\)-Hopf algebra. The author characterizes those \(C^\infty\)-Hopf algebras which are given by \(C^\infty(G)\) for some Lie group \(G\), obtaining thereby an anti-isomorphism between the category of compact Lie groups and the category of convenient Hopf algebras. Reviewer: Luboš Pick (Praha) Cited in 1 Document MSC: 16W30 Hopf algebras (associative rings and algebras) (MSC2000) 22E20 General properties and structure of other Lie groups 46E25 Rings and algebras of continuous, differentiable or analytic functions Keywords:\(C^\infty\)-Hopf algebras; compact Lie groups; dualities; categories of Hopf algebras PDF BibTeX XML Cite \textit{E. C. Farkas}, Commentat. Math. Univ. Carol. 41, No. 4, 651--661 (2000; Zbl 1051.16021) Full Text: EuDML OpenURL