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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A linear counterexample to the Fourteenth Problem of Hilbert in dimension eleven

Author: Gene Freudenburg
Journal: Proc. Amer. Math. Soc. 135 (2007), 51-57
MSC (2000): Primary 13A50, 14R20
Published electronically: July 28, 2006
MathSciNet review: 2280174
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Abstract: A family of $ \mathbb{G}_a$-actions on affine space $ \mathbb{A}^m$ is constructed, each having a non-finitely generated ring of invariants ($ m\ge 6$). Because these actions are of small degree, they induce linear actions of unipotent groups $ \mathbb{G}_a^n\rtimes\mathbb{G}_a$ on $ \mathbb{A}^{2n+3}$ for $ n\ge 4$, and these invariant rings are also non-finitely generated. The smallest such action presented here is for the group $ \mathbb{G}_a^4\rtimes\mathbb{G}_a$ acting linearly on $ \mathbb{A}^{11}$.

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Additional Information

Gene Freudenburg
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008

PII: S 0002-9939(06)08532-7
Keywords: Hilbert's Fourteenth Problem, invariant theory, locally nilpotent derivations
Received by editor(s): August 10, 2005
Published electronically: July 28, 2006
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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