Derksen, Harm; Kutzschebauch, Frank Nonlinearizable holomorphic group actions. (English) Zbl 0911.32042 Math. Ann. 311, No. 1, 41-53 (1998). The action of a complex reductive group \(G\) on \(\mathbb{C}^n\) is said to be linearizable if there exists a single automorphism of \(\mathbb{C}^n\) that conjugates \(G\) into \(GL(n,\mathbb{C})\subset \operatorname{Aut}_{\text{hol}}(\mathbb{C}^n)\).This problem has an complex algebraic analogue that has been studied by many authors. The main result of this paper is the following:Theorem. For every complex reductive Lie group \(G\) (except the trivial group) there exists a natural number \(N_G\) such that for all \(l\geq N_G\) there exists an effective non-linearizable holomorphic action of \(G\) on \(\mathbb{C}^l\). Reviewer: L.Barchini (Stillwater) Cited in 3 ReviewsCited in 15 Documents MSC: 32M05 Complex Lie groups, group actions on complex spaces 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 58B25 Group structures and generalizations on infinite-dimensional manifolds Keywords:nonlinearizable holomorphic group actions PDFBibTeX XMLCite \textit{H. Derksen} and \textit{F. Kutzschebauch}, Math. Ann. 311, No. 1, 41--53 (1998; Zbl 0911.32042) Full Text: DOI