On Observable Subgroups of Complex Analytic Groups and Algebraic Structures on Analytic Homogeneous Spaces
Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 495-502
Voir la notice de l'article provenant de la source Heldermann Verlag
Let L be a closed analytic subgroup of a faithfully representable complex analytic group G, let R(G) be the algebra of complex analytic representative functions on G, and let G0 be the universal algebraic subgroup (or algebraic kernel) of G.
In this paper, we show many characterizations of the property that the homogenous space G/L is (representationally) separable, i.e, R(G)L separates the points of G/L. This yield new characterizations for the observability of L in G and new characterizations for the existence of a quasi-affine structure on G/L. For example, G/L is separable if and only if the intersection of G0 and L is an observable algebraic subgroup of G0. Moreover, L is observable in G if and only if G/L is separable and L0 is equal to the intersection of G0 and L.
Similarly, we discuss a weaker separability of G/L and the existence of a representative algebraic structure on it.
In this paper, we show many characterizations of the property that the homogenous space G/L is (representationally) separable, i.e, R(G)L separates the points of G/L. This yield new characterizations for the observability of L in G and new characterizations for the existence of a quasi-affine structure on G/L. For example, G/L is separable if and only if the intersection of G0 and L is an observable algebraic subgroup of G0. Moreover, L is observable in G if and only if G/L is separable and L0 is equal to the intersection of G0 and L.
Similarly, we discuss a weaker separability of G/L and the existence of a representative algebraic structure on it.
Classification :
22E10, 22E45, 22F30, 20G20, 14L15
Mots-clés : observable subgroups, faithfully representable complex analytic group, homogeneous space
Mots-clés : observable subgroups, faithfully representable complex analytic group, homogeneous space
N. Nahlus. On Observable Subgroups of Complex Analytic Groups and Algebraic Structures on Analytic Homogeneous Spaces. Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 495-502. http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a10/
@article{JOLT_2002_12_2_a10,
author = {N. Nahlus},
title = {On {Observable} {Subgroups} of {Complex} {Analytic} {Groups} and {Algebraic} {Structures} on {Analytic} {Homogeneous} {Spaces}},
journal = {Journal of Lie Theory},
pages = {495--502},
year = {2002},
volume = {12},
number = {2},
zbl = {1007.22015},
url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a10/}
}