On the holomorphic separability of discrete quotients of complex Lie groups
This article presents two examples. The first is a 4-dimensional complex homogeneous space \(X=G/\Gamma\) where \(\Gamma\) is a discrete subgroup of a connected complex Lie group \(G\). The author shows that there are enough holomorphic functions on \(X\) to separate points but that \(X\) cannot be imbedded as a closed submanifold of \(\mathbb{C}^ n\) (\(X\) is not Stein). The second is an 8-dimensional Stein manifold that has a holomorphic \(SL(2,\mathbb{R})\)-action such that the algebra of \(SL(2,\mathbb{R})\)-invariant functions is not isomorphic to the algebra of holomorphic functions on a Stein space. This is contrary to the situation for complex reductive Lie groups or compact Lie groups acting holomorphically on Stein spaces.
scientific article; zbMATH DE number 126417