Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13A50, 14R20

Retrieve articles in all journals with MSC (2000): 13A50, 14R20


Additional Information

Gene Freudenburg
Affiliation: Department of Mathematics, Western Michigan University, Kalamazoo, Michigan 49008
Email: gene.freudenburg@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08532-7
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.