Holomorphic Dirichlet Series in Several Variables.
A -Hopf algebra is a -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those -Hopf algebras which are given by the algebra of smooth functions on some compact Lie group , thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.