Infinite-dimensionality of the Automorphism Groups of Homogeneous Stein Manifolds

TL;DR

This paper proves that the automorphism group of certain homogeneous Stein manifolds in complex geometry is infinite-dimensional, highlighting the rich symmetry structure of these spaces.

Contribution

It establishes the infinite-dimensionality of automorphism groups for homogeneous Stein manifolds of dimension greater than one.

Findings

Automorphism groups are infinite-dimensional for these manifolds.

The result applies to Stein manifolds with a transitive holomorphic Lie group action.

This extends understanding of symmetry in complex geometric structures.

Abstract

We show that the group of holomorphic automorphisms of a Stein manifold X of dimension greater than 1 is infinite-dimensional, provided X is a homogeneous space of a holomorphic action of a complex Lie group.