Algebraic Subgroups of Lie Groups

Abstract: 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 representable real analytic group $G$ with which the Tannaka duality theorem is restated.

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