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Separating invariants for the basic $ {\mathbb{G}}_{a}$-actions

Authors: Jonathan Elmer and Martin Kohls
Journal: Proc. Amer. Math. Soc. 140 (2012), 135-146
MSC (2010): Primary 13A50, 13N15
Published electronically: July 13, 2011
MathSciNet review: 2833525
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Abstract: We explicitly construct a finite set of separating invariants for the basic $ {\mathbb{G}}_{a}$-actions. These are the finite dimensional indecomposable rational linear representations of the additive group $ {\mathbb{G}}_{a}$ of a field of characteristic zero, and their invariants are the kernel of the Weitzenböck derivation $ D_{n}=x_{0}\frac{\partial}{\partial{x_{1}}}+\ldots+ x_{n-1}\frac{\partial}{\partial{x_{n}}}$.

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Additional Information

Jonathan Elmer
Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW United Kingdom

Martin Kohls
Affiliation: Technische Universität München, Zentrum Mathematik-M11, Boltzmannstrasse 3, 85748 Garching, Germany

Keywords: Invariant theory, separating invariants, binary forms, locally nilpotent derivations, basic $\mathbb{G}_{a}$-actions, generalized hypergeometric series.
Received by editor(s): November 12, 2010
Published electronically: July 13, 2011
Communicated by: Harm Derksen
Article copyright: © Copyright 2011 American Mathematical Society

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