Journal of Lie Theory Vol. 12, No. 2, pp. 495502 (2002) 

On Observable Subgroups of Complex Analytic Groups and Algebraic Structures on Analytic Homogenous SpacesNazih NahlusNazih NahlusDepartment of Mathematics American University of Beirut Beirut, Lebanon nahlus@aub.edu.lb Abstract: Let $\srm L$ be a closed analytic subgroup of a faithfully representable complex analytic group $\srm G$, let $\srm R(G)$ be the algebra of complex analytic representative functions on $\srm G$, and let $\srm G_0$ be the universal algebraic subgroup (or algebraic kernel) of $\srm G$. In this paper, we show many characterizations of the property that the homogenous space $\srm G/L$ is (representationally) {\it separable}, i.e, $\srm R(G)^L$ separates the points of $\srm G/L$. This yield new characterizations for the observability of $\srm L$ in $\srm G$ and new characterizations for the existence of a quasiaffine structure on $\srm G/L$. For example, $\srm G/L$ is separable if and only if $\srm G_0 \cap\ L$ is an observable algebraic subgroup of $\srm G_0$. Moreover, $\srm L$ is observable in $\srm G$ if and only if $\srm G/L$ is separable and $\srm L_0 = G_0 \cap\ L$. Similarly, we discuss a weaker separability of $\srm G/L$ and the existence of a representative algebraic structure on it. Classification (MSC2000): 22E10, 22E45, 22F30, 20G20, 14L15 Full text of the article:
Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.
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