**Journal of Lie Theory
**

Vol. 9, No. 1, pp. 271-284 (1999)

#
Algebraic Subgroups of Lie Groups

##
D. H. Lee

Department of Mathematics

Case Western Reserve University

Cleveland, Ohio 44106, USA

dhl@po.cwru.edu

**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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