Duality for compact connected groups and semisimple Lie algebras

Abstract

We investigate the notion of duality for nonabelian compact groups. LetC be the category of all compact connected groupsG and of all isomorphisms. We show thatC is equivalent to the category of the dual objects\( \hat G \) endowed with a suitable class of isomorphisms. Finally we remark that the same statement is true for semisimple complex Lie algebras.