In this work, we introduce the notion of algebraic subgroups of complex Lie groups, and prove that every faithfully representable complex analytic group G admits an algebraic subgroup T (G) which is the largest in the sense that it contains all algebraic subgroups of G . Moreover, the rational representations of the algebraic subgroup T (G) are exactly the restrictions to T (G) of all complex analytic representations of G . This enables us to single out a certain subgroup of a faithfully… CONTINUE READING