Journal article

Andersén-Lempert-theory with parameters: a representation theoretic point of view

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Author list: Kutzschebauch, Frank

Publication year: 2005

Start page: 325

End page: 340

Number of pages: 16

ISSN: 0219-4988

DOI: http://dx.doi.org/10.1142/S0219498805001216


Abstract

We calculate the invariant subspaces in the linear representation of the group of algebraic automorphisms of Cn on the vector space of algebraic vector fields on Cn and more generally we do this in a setting with parameter. As an application to the field of Several Complex Variables we get a new proof of the Andersén–Lempert observation and a parametric version of the Andersén–Lempert theorem. Further applications to the question of embeddings of Ck into Cn are announced.


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