Abstract
Various algebraic and geometric conditions on connected complex Lie groups G and H are shown to characterize the quotient G/H as a Stein manifold. Among these conditions are analytic analogues of the algebraic notions of observable or strongly observable subgroups and cohomological conditions expressed in terms of equivariant maps. A specific group theoretic condition on H, generalizing Matsushima's criterion for reductive groups, is shown to be necessary for G/H to be Stein and the sufficiency of this condition is proven when G is solvable or when H satisfies a dimension restriction. Also included is a geometric description of a Stein quotient G/H as a bundle space over an orbit of a maximal reductive subgroup of G, and a theorem on the orbits of solvable groups In ℂn.
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Dedicated to Prof. Karl Stein
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Snow, D.M. Stein quotients of connected complex lie groups. Manuscripta Math 50, 185–214 (1985). https://doi.org/10.1007/BF01168831
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DOI: https://doi.org/10.1007/BF01168831